Finite Group Databasebeta

← #34113159

Subgroups — #34113159

Order 20096.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757992C211yesmaximal, characteristic, complemented
2#23757944C211yesmaximal, characteristic, complemented
3#23757663C211yesmaximal, characteristic, complemented
4#23757661C211yesmaximal, characteristic, complemented
5#23757644C211yesmaximal, characteristic, complemented
6#23757487C211yesmaximal, characteristic, complemented
7#23757477C211yesmaximal, characteristic, complemented
8#23757474C211yesmaximal, characteristic, complemented
9#23757471C211yesmaximal, characteristic, complemented
10#23757466C211yesmaximal, characteristic, complemented
11#23757402C211yesmaximal, characteristic, complemented
12#23757376C211yesmaximal, characteristic, complemented
13#23757373C211yesmaximal, characteristic, complemented
14#23757353C211yesmaximal, characteristic, complemented
15#463×C157C211yesmaximal, characteristic, complemented
16C2×#14578954—21no—
17C2×#14578943C2211yescharacteristic
18C2×#14578943C2211yescharacteristic
19C2×#14578942C2211yescharacteristic
20C2×#14578941C2211yescharacteristic
21C2×#14578941C2211yescharacteristic
22C2×#14578939C2211yescharacteristic
23C2×#14578939C2211yescharacteristic
24#19097769C2211yescharacteristic
25#19097768C2211yescharacteristic
26#19097767C2211yescharacteristic
27#19097767C2211yescharacteristic
28#19097764—21no—
29#19097764—21no—
30#19097758C2211yescharacteristic
31#19097748—21no—
32#19097745—21no—
33#19097744—21no—
34#19097744—21no—
35Q8×Dic157C2211yescharacteristic
36C4×Dic314C2211yescharacteristic
37C4×Dic314C2211yescharacteristic
38D4×Dic157C2211yescharacteristic
39#19097733C2211yescharacteristic
40#19097733C2211yescharacteristic
41#19097727—21no—
42#19097704C2211yescharacteristic
43#19097700C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097694C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097692C2211yescharacteristic
49#19097682C2211yescharacteristic
50#19097681C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52C2×SD16×C157C2211yescharacteristic
53C2×D8×C157C2211yescharacteristic
54#124×C157C2211yescharacteristic
55C4×D4×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59#14578954—44no—
60C2×Dic314D411yescharacteristic
61C2×Dic314C2311yescharacteristic
62C2×D628—21no—
63C2×D628—21no—
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C22×Dic157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73#14578943—41no—
74#14578943—41no—
75#14578942—22no—
76#14578941—22no—
77#14578941—41no—
78#14578939—22no—
79#14578939—41no—
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C4⋊Dic157—21no—
83C4⋊Dic157D411yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933D411yescharacteristic
89#14578933D411yescharacteristic
90C22⋊Dic157—21no—
91C22⋊Dic157—21no—
92C22⋊Dic157—21no—
93#14578931—21no—
94#14578931—21no—
95C4×Dic157—21no—
96C4×Dic157—21no—
97C4×Dic157C2311yescharacteristic
98C4×Dic157C2311yescharacteristic
99C2×Q8×C157C2311yescharacteristic
100C2×D4×C157C2311yescharacteristic
101C2×D4×C157C2311yescharacteristic
102C22×C4×C157—21no—
103SD16×C157—41no—
104D8×C157—41no—
105C2×C8×C157C2311yescharacteristic
106C2×C8×C157C2311yescharacteristic
107C4⋊C4×C157C2311yescharacteristic
108C22⋊C4×C157—21no—
109C22⋊C4×C157—21no—
110C22⋊C4×C157—21no—
111C42×C157C2311yescharacteristic
112C22×D157—21no—
113C22×D157—21no—
114Dic314—22no—
115Dic314—21no—
116Dic314—21no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—21no—
121D628—42no—
122D628—81no—
123C22⋊D157—42no—
124C22⋊D157—42no—
125C22⋊D157—81no—
126C22⋊D157—81no—
127C2×Dic157—21no—
128C2×Dic157—21no—
129C2×Dic157—42no—
130C2×Dic157C2×D411yescharacteristic
131C2×Dic157C2×D411yescharacteristic
132C2×Dic157C2×D411yescharacteristic
133C2×Dic157C2×D411yescharacteristic
134C4×D157—42no—
135C4×D157—42no—
136#11929434—21no—
137#11929434#4112yescomplemented
138C23×C157—21no—
139C23×C157—21no—
140Q8×C157—21no—
141Q8×C157—21no—
142D4×C157—21no—
143D4×C157—21no—
144D4×C157—21no—
145D4×C157—21no—
146C2×C4×C157—21no—
147C2×C4×C157—21no—
148C2×C4×C157—42no—
149C2×C4×C157C2×D411yescharacteristic
150C2×C4×C157C2×D411yescharacteristic
151C2×C4×C157C2411yescharacteristic
152C8×C157—21no—
153C8×C157—21no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157—41no—
158C22×C157—41no—
159C22×C157—41no—
160C22×C157C22×D411yescharacteristic
161C2×D157—41no—
162C2×D157—41no—
163C2×D157—41no—
164C2×D157—41no—
165C2×D157—41no—
166C2×D157—41no—
167C4×C157—21no—
168C4×C157—21no—
169C4×C157—41no—
170C4×C157—41no—
171C4×C157C2×#4111yescharacteristic
172C4×C157H(5,𝔽2)11yescharacteristic
173Dic157—21no—
174Dic157—21no—
175Dic157—21no—
176Dic157—41no—
177Dic157—41no—
178Dic157AGL(1,ℤ/8)12yes—
179C2×C157—81no—
180C2×C157—81no—
181C2×C157#55011yescharacteristic
182C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C157#57711yescharacteristic
184D157—81no—
185D157—81no—
186C157#339711yescharacteristic, complemented, Sylow
187#3397—1571nomaximal, Sylow
188#556—1571no—
189#550—1571no—
190#496—1571no—
191#496—1571no—
192#492—1571no—
193#463—1571no—
194#463D15711yescharacteristic, complemented
195#461—1571no—
196#460—1571no—
197#460—1571no—
198#459—1571no—
199#446—1571no—
200#440—1571no—
201#440—1571no—
202C4×D8—1571no—
203C2×#41—3141no—
204C2×SD16—1571no—
205C2×SD16—1571no—
206C2×SD16—1571no—
207C2×SD16—1571no—
208C2×SD16—1571no—
209C2×SD16C2×D15711yescharacteristic
210C2×D8—1571no—
211C2×D8—1571no—
212C2×D8C2×D15711yescharacteristic
213C4⋊Q8—1571no—
214#127—1571no—
215#127—1571no—
216#127—1571no—
217#126—3141no—
218#126—3141no—
219#124—1571no—
220#124C2×D15711yescharacteristic
221C22⋊Q8—3141no—
222#121—3141no—
223#121—3141no—
224#121—3141no—
225C4×Q8—1571no—
226C4×Q8—1571no—
227C4×Q8—1571no—
228C4×D4—1571no—
229C4×D4—1571no—
230C4×D4—1571no—
231C4×D4C2×D15711yescharacteristic
232#117—3141no—
233#107—1571no—
234C4⋊C8—1571no—
235C4⋊C8—1571no—
236C4⋊C8C2×D15711yescharacteristic
237#103—1571no—
238#103C2×D15711yescharacteristic
239#102—1571no—
240#102—1571no—
241#102—1571no—
242#102C2×D15711yescharacteristic
243#97—1571no—
244#97—1571no—
245C4×C8—1571no—
246#41—6284no—
247C2×Q8—1571no—
248C2×Q8—1571no—
249C2×Q8C22×D15711yescharacteristic
250C2×D4—3141no—
251C2×D4—3141no—
252C2×D4—3141no—
253C2×D4—3141no—
254C2×D4—3141no—
255C2×D4—3141no—
256C2×D4—1571no—
257C2×D4—1571no—
258C2×D4C22×D15711yescharacteristic
259C2×D4C22×D15711yescharacteristic
260C22×C4—21no—
261C22×C4—3141no—
262C22×C4—3141no—
263C22×C4—3141no—
264SD16—41no—
265SD16—3142no—
266SD16—3142no—
267SD16—6281no—
268SD16—6281no—
269SD16—6281no—
270D8—41no—
271D8—3142no—
272D8—6281no—
273C2×C8—1571no—
274C2×C8—1571no—
275C2×C8C22×D15711yescharacteristic
276C2×C8C22×D15711yescharacteristic
277C4⋊C4—3141no—
278C4⋊C4—3141no—
279C4⋊C4—3141no—
280C4⋊C4—3141no—
281C4⋊C4—1571no—
282C4⋊C4—1571no—
283C4⋊C4—1571no—
284C4⋊C4—1571no—
285C4⋊C4C22×D15711yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—3141no—
290C22⋊C4—3141no—
291C22⋊C4—3141no—
292C22⋊C4—3141no—
293C22⋊C4—3141no—
294C42—3141no—
295C42—3141no—
296C42—1571no—
297C42—1571no—
298C42C22×D15711yescharacteristic
299C23—21no—
300C23—21no—
301C23—3141no—
302C23—3141no—
303Q8—21no—
304Q8—21no—
305Q8—3142no—
306Q8—3141no—
307Q8—3141no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—3141no—
313D4—3141no—
314D4—3141no—
315D4—3141no—
316D4—6282no—
317D4—6282no—
318D4—6282no—
319D4—12561no—
320D4—12561no—
321D4—12561no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—3141no—
326C2×C4—3141no—
327C2×C4—6282no—
328C2×C4—6282no—
329C2×C4—6282no—
330C2×C4—1571no—
331C2×C4—1571no—
332C2×C4—1571no—
333C2×C4—1571no—
334C2×C4D4×D15711yescharacteristic
335C2×C4D4×D15711yescharacteristic
336C2×C4C23×D15711yescharacteristic
337C8—21no—
338C8—21no—
339C8—3141no—
340C8—1572no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—6281no—
348C22—6281no—
349C22—6281no—
350C22—6281no—
351C22—6281no—
352C22—6281no—
353C22C2×D4×D15711yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—3141no—
359C4—3141no—
360C4—3141no—
361C4—6281no—
362C4—6281no—
363C4—1572no—
364C4#41×D15711yescharacteristic
365C4#1909781611yescharacteristic
366C2—81no—
367C2—81no—
368C2—12561no—
369C2—12561no—
370C2#2375794111yescharacteristic
371C2AGL(1,ℤ/8)×D15711yescharacteristic
372C2#2375808011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#463×C157C2
socleC22×C157C22×D4
hypercenter#463D157
hypocenterC157#3397
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #23757992C2semidirect
2. #23757944C2semidirect
3. #23757663C2semidirect
4. #23757661C2semidirect
5. #23757644C2semidirect
6. #23757487C2semidirect
7. #23757477C2semidirect
8. #23757474C2semidirect
9. #23757471C2semidirect
10. #23757466C2semidirect
11. #23757402C2semidirect
12. #23757376C2semidirect
13. #23757373C2semidirect
14. #23757353C2semidirect
15. #463×C157C2semidirect
137. #11929434#41semidirect
186. C157#3397semidirect
194. #463D157semidirect

Maximal subgroups

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

subgroupindex
#237579922
#237579442
#237576632
#237576612
#237576442
#237574872
#237574772
#237574742
#237574712
#237574662
#237574022
#237573762
#237573732
#237573532
#463×C1572
#3397157