Finite Group Databasebeta

← #34112140

Subgroups — #34112140

Order 20096.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757967C211yesmaximal, characteristic, complemented
2#23757941C211yesmaximal, characteristic, complemented
3#23757636C211yesmaximal, characteristic, complemented
4#23757588C211yesmaximal, characteristic, complemented
5#23757583C211yesmaximal, characteristic, complemented
6#23757527C211yesmaximal, characteristic, complemented
7#23757507C211yesmaximal, characteristic, complemented
8#23757467C211yesmaximal, characteristic, complemented
9#23757420C211yesmaximal, characteristic, complemented
10#23757419C211yesmaximal, characteristic, complemented
11#23757372C211yesmaximal, characteristic, complemented
12#23757341C211yesmaximal, characteristic, complemented
13#23757271C211yesmaximal, characteristic, complemented
14#23757267C211yesmaximal, characteristic, complemented
15#482×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578953C2211yescharacteristic
18C2×#14578943C2211yescharacteristic
19C2×D1256C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21C2×#14578937C2211yescharacteristic
22C22×#11929434C2211yescharacteristic
23#19097767—21no—
24#19097767C2211yescharacteristic
25#19097765—21no—
26#19097762C2211yescharacteristic
27#19097753—21no—
28#19097746C2211yescharacteristic
29#19097746C2211yescharacteristic
30#19097745C2211yescharacteristic
31#19097744—21no—
32#19097744—21no—
33#19097743—21no—
34#19097736C2211yescharacteristic
35C4×D628—21no—
36#19097733C2211yescharacteristic
37C4×C22⋊D157C2211yescharacteristic
38#19097731—21no—
39C4⋊C4×D157C2211yescharacteristic
40#19097704C2211yescharacteristic
41#19097700C2211yescharacteristic
42#19097696C2211yescharacteristic
43#19097694C2211yescharacteristic
44#19097694C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097691C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097681C2211yescharacteristic
52#121×C157C2211yescharacteristic
53#117×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58C22⋊C8×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—41no—
61#14578953—22no—
62#14578953—41no—
63C2×Dic314C2311yescharacteristic
64C2×D628—21no—
65C2×D628—21no—
66C2×D628C2311yescharacteristic
67C2×D628C2311yescharacteristic
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157D411yescharacteristic
74C22×Dic157—21no—
75C2×C4×D157—21no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157C2311yescharacteristic
79#14578943—22no—
80D1256—41no—
81#14578939—41no—
82#14578937—41no—
83C2×#11929434—41no—
84C2×#11929434C2311yescharacteristic
85C2×#11929434C2311yescharacteristic
86C4⋊Dic157—21no—
87C4⋊Dic157C2311yescharacteristic
88#14578933—21no—
89#14578933—21no—
90#14578933—21no—
91#14578933D411yescharacteristic
92C22⋊Dic157D411yescharacteristic
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96#14578931—21no—
97#14578931D411yescharacteristic
98C4×Dic157—21no—
99C4×Dic157C2311yescharacteristic
100C2×D4×C157—21no—
101C2×D4×C157C2311yescharacteristic
102C22×C4×C157C2311yescharacteristic
103C2×C8×C157C2311yescharacteristic
104C2×C8×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C4⋊C4×C157C2311yescharacteristic
107C4⋊C4×C157C2311yescharacteristic
108C22⋊C4×C157—21no—
109C22⋊C4×C157—21no—
110C42×C157—21no—
111C22×D157—21no—
112C22×D157—21no—
113C22×D157C2×D411yescharacteristic
114Dic314—21no—
115Dic314#4112yes—
116D628—21no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—42no—
121D628—81no—
122C22⋊D157—41no—
123C22⋊D157—42no—
124C22⋊D157—42no—
125C22⋊D157—42no—
126C22⋊D157—81no—
127C22⋊D157—81no—
128C2×Dic157—21no—
129C2×Dic157—21no—
130C2×Dic157—42no—
131C2×Dic157C2×D411yescharacteristic
132C2×Dic157C2×D411yescharacteristic
133C2×Dic157C2×D411yescharacteristic
134C4×D157—21no—
135C4×D157—21no—
136C4×D157—42no—
137C4×D157—81no—
138C4×D157—81no—
139#11929434—21no—
140#11929434—21no—
141C23×C157—21no—
142C23×C157C2×D411yescharacteristic
143D4×C157—21no—
144D4×C157—21no—
145D4×C157—81no—
146C2×C4×C157—21no—
147C2×C4×C157—21no—
148C2×C4×C157—21no—
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157C2×D411yescharacteristic
152C2×C4×C157C2411yescharacteristic
153C8×C157—21no—
154C8×C157—21no—
155C22×C157—21no—
156C22×C157—21no—
157C22×C157—21no—
158C22×C157—41no—
159C22×C157—41no—
160C22×C157—41no—
161C22×C157C22×D411yescharacteristic
162C2×D157—21no—
163C2×D157—21no—
164C2×D157—21no—
165C2×D157—41no—
166C2×D157—41no—
167C2×D157—41no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C4×C157—21no—
172C4×C157—41no—
173C4×C157—41no—
174C4×C157—41no—
175C4×C157C2×#4111yescharacteristic
176C4×C157H(5,𝔽2)11yescharacteristic
177Dic157—21no—
178Dic157—22no—
179Dic157—21no—
180Dic157—21no—
181Dic157—41no—
182C2×C157—41no—
183C2×C157—81no—
184C2×C157#54611yescharacteristic
185C2×C157#57511yescharacteristic
186C2×C157#57611yescharacteristic
187D157—41no—
188D157—81no—
189D157—81no—
190C157#330911yescharacteristic, complemented, Sylow
191#3309—1571nomaximal, Sylow
192#553—1571no—
193#550—1571no—
194#490—1571no—
195#482D15711yescharacteristic, complemented
196#480—1571no—
197#479—1571no—
198#469—1571no—
199#466—1571no—
200#459—1571no—
201#449—1571no—
202#449—1571no—
203#440—1571no—
204#435—1571no—
205#417—1571no—
206#416—1571no—
207C2×#41—1571no—
208C2×#41—1571no—
209C2×SD16—1571no—
210C2×D8—1571no—
211C2×D8—1571no—
212C2×M16—1571no—
213C22×C8—1571no—
214#127—3141no—
215#127—1571no—
216#126—3141no—
217#125—1571no—
218#123—3141no—
219#121—3141no—
220#121—3141no—
221#121—3141no—
222#121—1571no—
223#121—1571no—
224#121—1571no—
225#121C2×D15711yescharacteristic
226C4×Q8—1571no—
227C4×D4—3141no—
228C4×D4—3141no—
229C4×D4—1571no—
230C4×D4—1571no—
231#117C2×D15711yescharacteristic
232C2×C4⋊C4—1571no—
233#107—1571no—
234#107C2×D15711yescharacteristic
235#106C2×D15711yescharacteristic
236C4⋊C8—1571no—
237#103—1571no—
238#103—1571no—
239#103—1571no—
240#102—1571no—
241#102—1571no—
242#102—1571no—
243#102—1571no—
244#102—1571no—
245#102C2×D15711yescharacteristic
246#102C2×D15711yescharacteristic
247C22⋊C8—1571no—
248C22⋊C8C2×D15711yescharacteristic
249#97—1571no—
250#41—3142no—
251#41—3142no—
252#41—6281no—
253#41—6281no—
254C2×Q8—1571no—
255C2×D4—21no—
256C2×D4—3141no—
257C2×D4—3141no—
258C2×D4—3141no—
259C2×D4—3141no—
260C2×D4—3141no—
261C2×D4—3141no—
262C2×D4—3141no—
263C2×D4—1571no—
264C2×D4—1571no—
265C2×D4—1571no—
266C2×D4C22×D15711yescharacteristic
267C22×C4—3141no—
268C22×C4—3141no—
269C22×C4—3141no—
270C22×C4—3141no—
271C22×C4—1571no—
272C22×C4C22×D15711yescharacteristic
273SD16—3142no—
274D8—6281no—
275D8—6281no—
276M16—6281no—
277C2×C8—6281no—
278C2×C8—1571no—
279C2×C8—1571no—
280C2×C8C22×D15711yescharacteristic
281C2×C8C22×D15711yescharacteristic
282C4⋊C4—3141no—
283C4⋊C4—3141no—
284C4⋊C4—3141no—
285C4⋊C4—3141no—
286C4⋊C4—1571no—
287C4⋊C4—1571no—
288C4⋊C4C22×D15711yescharacteristic
289C4⋊C4C22×D15711yescharacteristic
290C4⋊C4C22×D15711yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—3141no—
294C22⋊C4—3141no—
295C22⋊C4—3141no—
296C22⋊C4—3141no—
297C22⋊C4—1571no—
298C22⋊C4—1571no—
299C42—21no—
300C42—3141no—
301C42—1571no—
302C23—21no—
303C23—3141no—
304C23—3141no—
305C23—1571no—
306C23D4×D15711yescharacteristic
307Q8—3141no—
308Q8—1572no—
309D4—21no—
310D4—21no—
311D4—81no—
312D4—3141no—
313D4—3141no—
314D4—3141no—
315D4—3141no—
316D4—6282no—
317D4—6281no—
318D4—6282no—
319D4—6282no—
320D4—6282no—
321D4—12561no—
322D4—12561no—
323D4—12561no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3141no—
330C2×C4—3141no—
331C2×C4—3141no—
332C2×C4—3141no—
333C2×C4—6282no—
334C2×C4—6282no—
335C2×C4—1571no—
336C2×C4—1571no—
337C2×C4—1571no—
338C2×C4—12561no—
339C2×C4—12561no—
340C2×C4D4×D15711yescharacteristic
341C2×C4C23×D15711yescharacteristic
342C8—21no—
343C8—21no—
344C8—3141no—
345C8—3141no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—3141no—
353C22—3141no—
354C22—3141no—
355C22—6281no—
356C22—6281no—
357C22—6281no—
358C22—6281no—
359C22—6281no—
360C22—6281no—
361C22C2×D4×D15711yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—3141no—
367C4—3142no—
368C4—3141no—
369C4—3141no—
370C4—6281no—
371C4#41×D15711yescharacteristic
372C4#1909781711yescharacteristic
373C2—41no—
374C2—81no—
375C2—6281no—
376C2—12561no—
377C2—12561no—
378C2#2375791511yescharacteristic
379C2#2375807011yescharacteristic
380C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#482×C157C2
socleC22×C157C22×D4
hypercenter#482D157
hypocenterC157#3309
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23757967C2semidirect
2. #23757941C2semidirect
3. #23757636C2semidirect
4. #23757588C2semidirect
5. #23757583C2semidirect
6. #23757527C2semidirect
7. #23757507C2semidirect
8. #23757467C2semidirect
9. #23757420C2semidirect
10. #23757419C2semidirect
11. #23757372C2semidirect
12. #23757341C2semidirect
13. #23757271C2semidirect
14. #23757267C2semidirect
15. #482×C157C2semidirect
190. C157#3309semidirect
195. #482D157semidirect

Maximal subgroups

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

subgroupindex
#237579672
#237579412
#237576362
#237575882
#237575832
#237575272
#237575072
#237574672
#237574202
#237574192
#237573722
#237573412
#237572712
#237572672
#482×C1572
#3309157