Finite Group Databasebeta

← #34110342

Subgroups — #34110342

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#23757879C211yesmaximal, characteristic, complemented
2#23757755C211yesmaximal, characteristic, complemented
3#23757593C211yesmaximal, characteristic, complemented
4#23757588C211yesmaximal, characteristic, complemented
5#23757570C211yesmaximal, characteristic, complemented
6#23757473C211yesmaximal, characteristic, complemented
7#23757469C211yesmaximal, characteristic, complemented
8#23757421C211yesmaximal, characteristic, complemented
9#23757421C211yesmaximal, characteristic, complemented
10#23757384C211yesmaximal, characteristic, complemented
11#23757376C211yesmaximal, characteristic, complemented
12#23757358C211yesmaximal, characteristic, complemented
13#23757355C211yesmaximal, characteristic, complemented
14#23757333C211yesmaximal, characteristic, complemented
15#479×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578941C2211yescharacteristic
18C2×#14578941C2211yescharacteristic
19C2×D1256C2211yescharacteristic
20C2×D1256C2211yescharacteristic
21#19097768C2211yescharacteristic
22#19097756—21no—
23#19097756—21no—
24#19097746—21no—
25#19097746—21no—
26#19097746C2211yescharacteristic
27#19097746C2211yescharacteristic
28Q8×Dic157C2211yescharacteristic
29C4×D628—21no—
30C4×D628C2211yescharacteristic
31#19097733—21no—
32#19097733C2211yescharacteristic
33#19097733C2211yescharacteristic
34#19097733C2211yescharacteristic
35#19097728—21no—
36#19097728C2211yescharacteristic
37C4⋊C4×D157—21no—
38C4⋊C4×D157C2211yescharacteristic
39#19097704C2211yescharacteristic
40#19097702C2211yescharacteristic
41C4⋊#11929434C2211yescharacteristic
42#19097693C2211yescharacteristic
43#19097693C2211yescharacteristic
44#19097691C2211yescharacteristic
45#19097691C2211yescharacteristic
46#19097691C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097683C2211yescharacteristic
49#19097683C2211yescharacteristic
50#19097681C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52#125×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58#103×C157C2211yescharacteristic
59#14578955—22no—
60#14578955—22no—
61C2×D628—21no—
62C2×D628—21no—
63C2×D628—21no—
64C2×D628—21no—
65C2×D628—21no—
66C2×D628C2311yescharacteristic
67C2×D628C2311yescharacteristic
68C2×D628C2311yescharacteristic
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157C2311yescharacteristic
76#14578941—22no—
77#14578941—22no—
78D1256—22no—
79D1256—22no—
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C4⋊Dic157—21no—
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578933D411yescharacteristic
86#14578933D411yescharacteristic
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931D411yescharacteristic
94#14578931D411yescharacteristic
95C4×Dic157—21no—
96C4×Dic157C2311yescharacteristic
97C2×Q8×C157C2311yescharacteristic
98C2×C8×C157C2311yescharacteristic
99C2×C8×C157C2311yescharacteristic
100C4⋊C4×C157—21no—
101C4⋊C4×C157—21no—
102C4⋊C4×C157—21no—
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C42×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—21no—
110C22×D157—21no—
111C22×D157C2×D411yescharacteristic
112D628—24no—
113D628—21no—
114D628—21no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—81no—
119D628—81no—
120D628—81no—
121D628—81no—
122D628#4112yes—
123C2×Dic157—21no—
124C2×Dic157C2×D411yescharacteristic
125C2×Dic157C2×D411yescharacteristic
126C2×Dic157C2×D411yescharacteristic
127C4×D157—24no—
128C4×D157—21no—
129C4×D157—21no—
130C4×D157—81no—
131C4×D157—81no—
132C4×D157—81no—
133C4×D157—81no—
134C4×D157—81no—
135#11929434—21no—
136#11929434—21no—
137Q8×C157—21no—
138Q8×C157#4112yes—
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—21no—
148C22×C157C22×D411yescharacteristic
149C2×D157—21no—
150C2×D157—22no—
151C2×D157—21no—
152C2×D157—21no—
153C2×D157—41no—
154C2×D157—41no—
155C2×D157—41no—
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×C157—41no—
167C4×C157C2×#4111yescharacteristic
168C4×C157C2×#4111yescharacteristic
169Dic157—21no—
170Dic157—21no—
171Dic157—21no—
172Dic157—41no—
173C2×C157#52511yescharacteristic
174C2×C157#57611yescharacteristic
175C2×C157#57711yescharacteristic
176D157—41no—
177D157—42no—
178D157—81no—
179D157—81no—
180C157#311911yescharacteristic, complemented, Sylow
181#3119—1571nomaximal, Sylow
182#540—1571no—
183#520—1571no—
184#481—1571no—
185#480—1571no—
186#479D15711yescharacteristic, complemented
187#478—1571no—
188#460—1571no—
189#459—1571no—
190#449—1571no—
191#449—1571no—
192#442—1571no—
193#440—1571no—
194C4×SD16—1571no—
195C4×D8—1571no—
196#433—1571no—
197C2×#41—1571no—
198C2×SD16—1571no—
199C2×SD16—1571no—
200C2×D8—1571no—
201C2×D8—1571no—
202#127—1571no—
203#125C2×D15711yescharacteristic
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×D4—1571no—
218#117—3141no—
219#117—1571no—
220C2×C4⋊C4—3141no—
221C2×C4⋊C4—1571no—
222#107—1571no—
223#107C2×D15711yescharacteristic
224#106—1571no—
225#106C2×D15711yescharacteristic
226C4⋊C8—1571no—
227C4⋊C8C2×D15711yescharacteristic
228#103C2×D15711yescharacteristic
229#103C2×D15711yescharacteristic
230#102—1571no—
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#102—1571no—
235#102—1571no—
236C22⋊C8—1571no—
237C22⋊C8—1571no—
238#97—1571no—
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×D4—1571no—
251C22×C4—3141no—
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4—1571no—
258SD16—3142no—
259SD16—3142no—
260D8—3142no—
261D8—3142no—
262C2×C8—1571no—
263C2×C8—1571no—
264C2×C8C22×D15711yescharacteristic
265C2×C8C22×D15711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—3141no—
270C4⋊C4—3141no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4—1571no—
274C4⋊C4C22×D15711yescharacteristic
275C4⋊C4C22×D15711yescharacteristic
276C4⋊C4C22×D15711yescharacteristic
277C22⋊C4—3141no—
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—3141no—
290C23—3141no—
291C23—3141no—
292C23—1571no—
293Q8—21no—
294Q8#1457895512yes—
295D4—3144no—
296D4—3141no—
297D4—3141no—
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—21no—
310C2×C4—3144no—
311C2×C4—3141no—
312C2×C4—3141no—
313C2×C4—3141no—
314C2×C4—1571no—
315C2×C4—1571no—
316C2×C4—1571no—
317C2×C4—12561no—
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—3141no—
330C22—3141no—
331C22—3142no—
332C22—3141no—
333C22—6281no—
334C22—6281no—
335C22—6281no—
336C22—6281no—
337C22—6281no—
338C22—6281no—
339C22—6281no—
340C22—6281no—
341C22C2×D4×D15711yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3141no—
349C4—3141no—
350C4—3141no—
351C4—6281no—
352C4#41×D15711yescharacteristic
353C4C2×#1457895511yescharacteristic
354C2—6281no—
355C2—6282no—
356C2—12561no—
357C2—12561no—
358C2#2375778611yescharacteristic
359C2#2375807511yescharacteristic
360C2#2375808211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#479×C157C2
socleC22×C157C22×D4
hypercenter#479D157
hypocenterC157#3119
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23757879C2semidirect
2. #23757755C2semidirect
3. #23757593C2semidirect
4. #23757588C2semidirect
5. #23757570C2semidirect
6. #23757473C2semidirect
7. #23757469C2semidirect
8. #23757421C2semidirect
9. #23757421C2semidirect
10. #23757384C2semidirect
11. #23757376C2semidirect
12. #23757358C2semidirect
13. #23757355C2semidirect
14. #23757333C2semidirect
15. #479×C157C2semidirect
180. C157#3119semidirect
186. #479D157semidirect

Maximal subgroups

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

subgroupindex
#237578792
#237577552
#237575932
#237575882
#237575702
#237574732
#237574692
#237574212
#237573842
#237573762
#237573582
#237573552
#237573332
#479×C1572
#3119157