Finite Group Databasebeta

← #34112144

Subgroups — #34112144

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#23757969C211yesmaximal, characteristic, complemented
2#23757944C211yesmaximal, characteristic, complemented
3#23757638C211yesmaximal, characteristic, complemented
4#23757598C211yesmaximal, characteristic, complemented
5#23757587C211yesmaximal, characteristic, complemented
6#23757581C211yesmaximal, characteristic, complemented
7#23757526C211yesmaximal, characteristic, complemented
8#23757509C211yesmaximal, characteristic, complemented
9#23757469C211yesmaximal, characteristic, complemented
10#23757420C211yesmaximal, characteristic, complemented
11#23757420C211yesmaximal, characteristic, complemented
12#23757375C211yesmaximal, characteristic, complemented
13#23757275C211yesmaximal, characteristic, complemented
14#23757270C211yesmaximal, characteristic, complemented
15#435×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578954C2211yescharacteristic
18C2×#14578943C2211yescharacteristic
19C2×D1256C2211yescharacteristic
20C2×D1256C2211yescharacteristic
21#19097768C2211yescharacteristic
22#19097767—21no—
23#19097766—21no—
24#19097763C2211yescharacteristic
25#19097753—21no—
26#19097745C2211yescharacteristic
27#19097745C2211yescharacteristic
28#19097745C2211yescharacteristic
29#19097745C2211yescharacteristic
30#19097744—21no—
31#19097744—21no—
32#19097743—21no—
33C4×Dic314C2211yescharacteristic
34C4×D628C2211yescharacteristic
35#19097733—21no—
36#19097731—21no—
37#19097730C2211yescharacteristic
38C2×C4⋊Dic157C2211yescharacteristic
39#19097705C2211yescharacteristic
40#19097705C2211yescharacteristic
41#19097703C2211yescharacteristic
42#19097696C2211yescharacteristic
43#19097696C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097693C2211yescharacteristic
49#19097693C2211yescharacteristic
50#19097693C2211yescharacteristic
51#19097693C2211yescharacteristic
52C2×M16×C157C2211yescharacteristic
53C22×C8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55C4⋊C8×C157C2211yescharacteristic
56C22⋊C8×C157C2211yescharacteristic
57C22⋊C8×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—22no—
61#14578954—41no—
62#14578954—41no—
63C2×Dic314C2311yescharacteristic
64C2×D628—21no—
65C2×D628—21no—
66C2×D628C2311yescharacteristic
67C2×D628C2311yescharacteristic
68C2×D628C2311yescharacteristic
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C22⋊D157—21no—
73C2×C22⋊D157—21no—
74C2×C22⋊D157—21no—
75C22×Dic157—21no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79#14578943—22no—
80D1256—41no—
81D1256—41no—
82C4⋊Dic157—21no—
83C4⋊Dic157C2311yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85C4⋊Dic157C2311yescharacteristic
86C4⋊Dic157C2311yescharacteristic
87#14578933—21no—
88#14578933—21no—
89#14578933—21no—
90C22⋊Dic157—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96C4×Dic157—21no—
97C4×Dic157—21no—
98C2×D4×C157D411yescharacteristic
99C22×C4×C157C2311yescharacteristic
100C22×C4×C157C2311yescharacteristic
101M16×C157—41no—
102C2×C8×C157—41no—
103C2×C8×C157C2311yescharacteristic
104C2×C8×C157C2311yescharacteristic
105C2×C8×C157C2311yescharacteristic
106C2×C8×C157C2311yescharacteristic
107C4⋊C4×C157D411yescharacteristic
108C22⋊C4×C157D411yescharacteristic
109C22⋊C4×C157D411yescharacteristic
110C42×C157C2311yescharacteristic
111C22×D157—21no—
112C22×D157—21no—
113C22×D157—21no—
114Dic314—21no—
115Dic314#4112yes—
116D628—21no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—21no—
121D628—21no—
122D628—42no—
123D628—81no—
124C22⋊D157—42no—
125C22⋊D157—42no—
126C22⋊D157—42no—
127C22⋊D157—81no—
128C22⋊D157—81no—
129C22⋊D157—81no—
130C2×Dic157—21no—
131C2×Dic157—21no—
132C2×Dic157—21no—
133C2×Dic157—21no—
134C2×Dic157—21no—
135C2×Dic157—81no—
136C4×D157—42no—
137C4×D157—42no—
138C4×D157—81no—
139C23×C157C2×D411yescharacteristic
140C23×C157C2×D411yescharacteristic
141D4×C157—41no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2×D411yescharacteristic
149C2×C4×C157C2×D411yescharacteristic
150C2×C4×C157C2411yescharacteristic
151C8×C157—21no—
152C8×C157—21no—
153C8×C157—21no—
154C8×C157—21no—
155C22×C157—21no—
156C22×C157—21no—
157C22×C157—21no—
158C22×C157—21no—
159C22×C157—21no—
160C22×C157—21no—
161C22×C157C22×D411yescharacteristic
162C2×D157—41no—
163C2×D157—41no—
164C2×D157—41no—
165C2×D157—41no—
166C2×D157—41no—
167C2×D157—41no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C4×C157—21no—
172C4×C157—21no—
173C4×C157—21no—
174C4×C157—21no—
175C4×C157C2×#4111yescharacteristic
176C4×C157H(5,𝔽2)11yescharacteristic
177Dic157—22no—
178Dic157—41no—
179Dic157—41no—
180Dic157—41no—
181Dic157—41no—
182C2×C157—41no—
183C2×C157—41no—
184C2×C157#54611yescharacteristic
185C2×C157#57511yescharacteristic
186C2×C157#57611yescharacteristic
187D157—81no—
188D157—81no—
189D157—81no—
190C157#330911yescharacteristic, complemented, Sylow
191#3309—1571nomaximal, Sylow
192#553—1571no—
193#550—1571no—
194#490—1571no—
195#482—1571no—
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#435D15711yescharacteristic, complemented
205#417—1571no—
206#416—1571no—
207C2×#41—1571no—
208C2×#41—1571no—
209C2×SD16—1571no—
210C2×D8—1571no—
211C2×D8—1571no—
212C2×M16C2×D15711yescharacteristic
213C22×C8C2×D15711yescharacteristic
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#121—1571no—
226C4×Q8—1571no—
227C4×D4—3141no—
228C4×D4—3141no—
229C4×D4—1571no—
230C4×D4C2×D15711yescharacteristic
231#117—1571no—
232C2×C4⋊C4—1571no—
233#107—1571no—
234#107—1571no—
235#106—1571no—
236C4⋊C8C2×D15711yescharacteristic
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#102—1571no—
246#102—1571no—
247C22⋊C8C2×D15711yescharacteristic
248C22⋊C8C2×D15711yescharacteristic
249#97C2×D15711yescharacteristic
250#41—3142no—
251#41—3142no—
252#41—6281no—
253#41—6281no—
254C2×Q8—1571no—
255C2×D4—3141no—
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×D4D62811yescharacteristic
267C22×C4—3141no—
268C22×C4—3141no—
269C22×C4—3141no—
270C22×C4—3141no—
271C22×C4C22×D15711yescharacteristic
272C22×C4C22×D15711yescharacteristic
273SD16—3142no—
274D8—6281no—
275D8—6281no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D15711yescharacteristic
279C2×C8C22×D15711yescharacteristic
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⋊C4—1571no—
289C4⋊C4—1571no—
290C4⋊C4D62811yescharacteristic
291C22⋊C4—3141no—
292C22⋊C4—3141no—
293C22⋊C4—3141no—
294C22⋊C4—3141no—
295C22⋊C4—3141no—
296C22⋊C4—3141no—
297C22⋊C4D62811yescharacteristic
298C22⋊C4D62811yescharacteristic
299C42—3141no—
300C42—3141no—
301C42C22×D15711yescharacteristic
302C23—3141no—
303C23—3141no—
304C23—3141no—
305C23C2×D62811yescharacteristic
306C23C2×D62811yescharacteristic
307Q8—3141no—
308Q8—1572no—
309D4—41no—
310D4—3141no—
311D4—3141no—
312D4—3141no—
313D4—3141no—
314D4—3141no—
315D4—3141no—
316D4—6282no—
317D4—6282no—
318D4—6282no—
319D4—6282no—
320D4—12561no—
321D4—12561no—
322D4—12561no—
323D4—12561no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—3141no—
329C2×C4—3141no—
330C2×C4—3141no—
331C2×C4—3141no—
332C2×C4—3141no—
333C2×C4—6282no—
334C2×C4—6282no—
335C2×C4—12561no—
336C2×C4—12561no—
337C2×C4C2×D62811yescharacteristic
338C2×C4C2×D62811yescharacteristic
339C2×C4C2×D62811yescharacteristic
340C2×C4C2×D62811yescharacteristic
341C2×C4C23×D15711yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—6281no—
353C22—6281no—
354C22—6281no—
355C22—6281no—
356C22—6281no—
357C22—6281no—
358C22—6281no—
359C22—6281no—
360C22—6281no—
361C22C22×D62811yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—3142no—
367C4—6281no—
368C4—6281no—
369C4—6281no—
370C4—6281no—
371C4#41×D15711yescharacteristic
372C4#1909781611yescharacteristic
373C2—41no—
374C2—41no—
375C2—12561no—
376C2—12561no—
377C2—12561no—
378C2#2375791811yescharacteristic
379C2#2375807311yescharacteristic
380C2#2375807811yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#435×C157C2
socleC22×C157C22×D4
hypercenter#435D157
hypocenterC157#3309
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #23757969C2semidirect
2. #23757944C2semidirect
3. #23757638C2semidirect
4. #23757598C2semidirect
5. #23757587C2semidirect
6. #23757581C2semidirect
7. #23757526C2semidirect
8. #23757509C2semidirect
9. #23757469C2semidirect
10. #23757420C2semidirect
11. #23757420C2semidirect
12. #23757375C2semidirect
13. #23757275C2semidirect
14. #23757270C2semidirect
15. #435×C157C2semidirect
190. C157#3309semidirect
204. #435D157semidirect

Maximal subgroups

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

subgroupindex
#237579692
#237579442
#237576382
#237575982
#237575872
#237575812
#237575262
#237575092
#237574692
#237574202
#237573752
#237572752
#237572702
#435×C1572
#3309157