Finite Group Databasebeta

← #34110333

Subgroups — #34110333

Order 20096.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757874C211yesmaximal, characteristic, complemented
2#23757755C211yesmaximal, characteristic, complemented
3#23757590C211yesmaximal, characteristic, complemented
4#23757588C211yesmaximal, characteristic, complemented
5#23757578C211yesmaximal, characteristic, complemented
6#23757576C211yesmaximal, characteristic, complemented
7#23757471C211yesmaximal, characteristic, complemented
8#23757467C211yesmaximal, characteristic, complemented
9#23757421C211yesmaximal, characteristic, complemented
10#23757417C211yesmaximal, characteristic, complemented
11#23757386C211yesmaximal, characteristic, complemented
12C4×#14578941C211yesmaximal, characteristic, complemented
13C4×#14578939C211yesmaximal, characteristic, complemented
14#23757335C211yesmaximal, characteristic, complemented
15#440×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578941C2211yescharacteristic
18C2×D1256C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20#19097767C2211yescharacteristic
21#19097762C2211yescharacteristic
22#19097754—21no—
23#19097753—21no—
24#19097746C2211yescharacteristic
25#19097745—21no—
26#19097744—21no—
27#19097742C2211yescharacteristic
28Q8×Dic157C2211yescharacteristic
29C4×D628—21no—
30C4×D628C2211yescharacteristic
31C4×D628C2211yescharacteristic
32#19097733—21no—
33#19097733C2211yescharacteristic
34#19097728—21no—
35#19097728C2211yescharacteristic
36C4⋊C4×D157—21no—
37C4⋊C4×D157C2211yescharacteristic
38#19097704C2211yescharacteristic
39#19097703C2211yescharacteristic
40#19097702C2211yescharacteristic
41#19097700C2211yescharacteristic
42#19097700C2211yescharacteristic
43#19097695C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097683C2211yescharacteristic
50#19097683C2211yescharacteristic
51C4×#11929434C2211yescharacteristic
52C2×SD16×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55#107×C157C2211yescharacteristic
56#103×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59#14578955—22no—
60#14578955—22no—
61C2×D628—21no—
62C2×D628—21no—
63C2×D628C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C4×D157—21no—
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157C2311yescharacteristic
74#14578941—22no—
75D1256—22no—
76#14578939—22no—
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C4⋊Dic157—21no—
80C4⋊Dic157—21no—
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85#14578933D411yescharacteristic
86#14578933D411yescharacteristic
87C22⋊Dic157—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931D411yescharacteristic
93#14578931D411yescharacteristic
94C4×Dic157—21no—
95C4×Dic157C2311yescharacteristic
96C2×Q8×C157C2311yescharacteristic
97C2×D4×C157C2311yescharacteristic
98C22×C4×C157—21no—
99SD16×C157—22no—
100C2×C8×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C4⋊C4×C157—21no—
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C22⋊C4×C157—21no—
106C42×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—21no—
110C22×D157C2×D411yescharacteristic
111D628—24no—
112D628—21no—
113D628—21no—
114D628—21no—
115D628—81no—
116D628#4112yes—
117C22⋊D157—81no—
118C22⋊D157—81no—
119C22⋊D157—81no—
120C2×Dic157—21no—
121C2×Dic157—21no—
122C2×Dic157C2×D411yescharacteristic
123C2×Dic157C2×D411yescharacteristic
124C2×Dic157C2×D411yescharacteristic
125C4×D157—24no—
126C4×D157—21no—
127C4×D157—21no—
128C4×D157—81no—
129C4×D157—81no—
130C4×D157—81no—
131C4×D157—81no—
132#11929434—21no—
133#11929434—21no—
134C23×C157—21no—
135Q8×C157—21no—
136Q8×C157#4112yes—
137D4×C157—21no—
138D4×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—81no—
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2411yescharacteristic
146C8×C157—21no—
147C8×C157—21no—
148C22×C157—41no—
149C22×C157—41no—
150C22×C157—41no—
151C22×C157C22×D411yescharacteristic
152C2×D157—21no—
153C2×D157—22no—
154C2×D157—21no—
155C2×D157—21no—
156C2×D157—41no—
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C4×C157—22no—
162C4×C157—21no—
163C4×C157—21no—
164C4×C157—41no—
165C4×C157—41no—
166C4×C157C2×#4111yescharacteristic
167C4×C157C2×#4111yescharacteristic
168Dic157—21no—
169Dic157—21no—
170Dic157—21no—
171Dic157—41no—
172Dic157—41no—
173C2×C157—81no—
174C2×C157#52511yescharacteristic
175C2×C157#57611yescharacteristic
176C2×C157#57711yescharacteristic
177D157—41no—
178D157—42no—
179D157—81no—
180C157#311911yescharacteristic, complemented, Sylow
181#3119—1571nomaximal, Sylow
182#540—1571no—
183#520—1571no—
184#481—1571no—
185#480—1571no—
186#479—1571no—
187#478—1571no—
188#460—1571no—
189#459—1571no—
190#449—1571no—
191#449—1571no—
192#442—1571no—
193#440D15711yescharacteristic, complemented
194C4×SD16—1571no—
195C4×D8—1571no—
196#433—1571no—
197C2×#41—1571no—
198C2×SD16—1571no—
199C2×SD16C2×D15711yescharacteristic
200C2×D8—1571no—
201C2×D8—1571no—
202#127—1571no—
203#125—1571no—
204#123—3141no—
205#123—3141no—
206#121—3141no—
207#121—3141no—
208#121—1571no—
209#121—1571no—
210C4×Q8—1571no—
211C4×Q8C2×D15711yescharacteristic
212C4×D4—3141no—
213C4×D4—3141no—
214C4×D4—1571no—
215C4×D4—1571no—
216C4×D4—1571no—
217C4×D4C2×D15711yescharacteristic
218#117—3141no—
219#117—1571no—
220C2×C4⋊C4—3141no—
221C2×C4⋊C4—1571no—
222#107—1571no—
223#107C2×D15711yescharacteristic
224#106—1571no—
225#106—1571no—
226C4⋊C8—1571no—
227C4⋊C8—1571no—
228#103—1571no—
229#103C2×D15711yescharacteristic
230#102—1571no—
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#102—1571no—
235#102C2×D15711yescharacteristic
236C22⋊C8—1571no—
237C22⋊C8—1571no—
238#97C2×D15711yescharacteristic
239C4×C8—1571no—
240#41—3142no—
241#41—3142no—
242C2×Q8C22×D15711yescharacteristic
243C2×D4—3141no—
244C2×D4—3141no—
245C2×D4—3141no—
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—1571no—
249C2×D4—1571no—
250C2×D4C22×D15711yescharacteristic
251C22×C4—21no—
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4—1571no—
258SD16—22no—
259SD16—3142no—
260D8—3142no—
261D8—3142no—
262C2×C8—1571no—
263C2×C8—1571no—
264C2×C8C22×D15711yescharacteristic
265C2×C8C22×D15711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3141no—
268C4⋊C4—3141no—
269C4⋊C4—3141no—
270C4⋊C4—3141no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4—1571no—
274C4⋊C4—1571no—
275C4⋊C4C22×D15711yescharacteristic
276C4⋊C4C22×D15711yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4—1571no—
284C22⋊C4—1571no—
285C42—21no—
286C42—3141no—
287C42—1571no—
288C42C22×D15711yescharacteristic
289C23—21no—
290C23—3141no—
291C23—3141no—
292C23—1571no—
293Q8—21no—
294Q8#1457895412yes—
295D4—21no—
296D4—21no—
297D4—3144no—
298D4—3141no—
299D4—3141no—
300D4—3141no—
301D4—1572no—
302D4—12561no—
303D4—12561no—
304D4—12561no—
305D4—12561no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—3144no—
311C2×C4—3141no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—3141no—
315C2×C4—1571no—
316C2×C4—1571no—
317C2×C4—1571no—
318C2×C4—12561no—
319C2×C4—12561no—
320C2×C4—12561no—
321C2×C4—12561no—
322C2×C4D4×D15711yescharacteristic
323C2×C4D4×D15711yescharacteristic
324C2×C4C23×D15711yescharacteristic
325C8—21no—
326C8—21no—
327C8—3141no—
328C8—3141no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3141no—
333C22—3141no—
334C22—3142no—
335C22—3141no—
336C22—6281no—
337C22—6281no—
338C22—6281no—
339C22—6281no—
340C22—6281no—
341C22C2×D4×D15711yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—3141no—
348C4—3141no—
349C4—3141no—
350C4—6281no—
351C4—6281no—
352C4#41×D15711yescharacteristic
353C4C2×#1457895411yescharacteristic
354C2—81no—
355C2—6281no—
356C2—6282no—
357C2—12561no—
358C2#2375778211yescharacteristic
359C2#2375807711yescharacteristic
360C2#2375808211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#440×C157C2
socleC22×C157C22×D4
hypercenter#440D157
hypocenterC157#3119
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23757874C2semidirect
2. #23757755C2semidirect
3. #23757590C2semidirect
4. #23757588C2semidirect
5. #23757578C2semidirect
6. #23757576C2semidirect
7. #23757471C2semidirect
8. #23757467C2semidirect
9. #23757421C2semidirect
10. #23757417C2semidirect
11. #23757386C2semidirect
12. C4×#14578941C2semidirect
13. C4×#14578939C2semidirect
14. #23757335C2semidirect
15. #440×C157C2semidirect
180. C157#3119semidirect
193. #440D157semidirect

Maximal subgroups

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

subgroupindex
#237578742
#237577552
#237575902
#237575882
#237575782
#237575762
#237574712
#237574672
#237574212
#237574172
#237573862
C4×#145789412
C4×#145789392
#237573352
#440×C1572
#3119157