Finite Group Databasebeta

← #34112137

Subgroups — #34112137

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#23757975C211yesmaximal, characteristic, complemented
2#23757941C211yesmaximal, characteristic, complemented
3#23757636C211yesmaximal, characteristic, complemented
4#23757599C211yesmaximal, characteristic, complemented
5#23757584C211yesmaximal, characteristic, complemented
6#23757583C211yesmaximal, characteristic, complemented
7#23757508C211yesmaximal, characteristic, complemented
8#23757466C211yesmaximal, characteristic, complemented
9#23757416C211yesmaximal, characteristic, complemented
10#23757415C211yesmaximal, characteristic, complemented
11#23757370C211yesmaximal, characteristic, complemented
12#23757342C211yesmaximal, characteristic, complemented
13#23757275C211yesmaximal, characteristic, complemented
14#23757266C211yesmaximal, characteristic, complemented
15#469×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578953C2211yescharacteristic
18C2×#14578942C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20C2×C8×D157C2211yescharacteristic
21#19097767—21no—
22#19097767C2211yescharacteristic
23#19097764—21no—
24#19097762C2211yescharacteristic
25#19097755—21no—
26#19097746C2211yescharacteristic
27#19097744—21no—
28#19097743—21no—
29#19097743—21no—
30#19097742C2211yescharacteristic
31#19097736C2211yescharacteristic
32D4×Dic157—21no—
33D4×Dic157C2211yescharacteristic
34C4×C22⋊D157C2211yescharacteristic
35#19097731—21no—
36#19097729C2211yescharacteristic
37C2×C4⋊Dic157C2211yescharacteristic
38#19097704C2211yescharacteristic
39#19097704C2211yescharacteristic
40#19097700C2211yescharacteristic
41#19097696C2211yescharacteristic
42#19097696C2211yescharacteristic
43#19097694C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097692C2211yescharacteristic
48#19097691C2211yescharacteristic
49C22⋊#11929434C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097681C2211yescharacteristic
52C2×D8×C157C2211yescharacteristic
53C2×M16×C157C2211yescharacteristic
54#121×C157C2211yescharacteristic
55#121×C157C2211yescharacteristic
56#106×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—41no—
61#14578953—22no—
62#14578953—41no—
63C2×Dic314C2311yescharacteristic
64C2×D628—21no—
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157D411yescharacteristic
72C22×Dic157—21no—
73C22×Dic157—21no—
74C22×Dic157—21no—
75C2×C4×D157—21no—
76C2×C4×D157C2311yescharacteristic
77#14578942—22no—
78#14578939—41no—
79C2×#11929434C2311yescharacteristic
80C2×#11929434C2311yescharacteristic
81C8×D157—41no—
82C4⋊Dic157—21no—
83C4⋊Dic157—21no—
84C4⋊Dic157C2311yescharacteristic
85C4⋊Dic157C2311yescharacteristic
86#14578933—21no—
87#14578933—21no—
88#14578933D411yescharacteristic
89C22⋊Dic157—21no—
90C22⋊Dic157—21no—
91C22⋊Dic157D411yescharacteristic
92#14578931—21no—
93#14578931—21no—
94#14578931D411yescharacteristic
95C4×Dic157—21no—
96C4×Dic157—21no—
97C4×Dic157C2311yescharacteristic
98C2×D4×C157—21no—
99C2×D4×C157—21no—
100C2×D4×C157C2311yescharacteristic
101C2×D4×C157C2311yescharacteristic
102C22×C4×C157C2311yescharacteristic
103D8×C157—41no—
104M16×C157—41no—
105C2×C8×C157C2311yescharacteristic
106C2×C8×C157C2311yescharacteristic
107C4⋊C4×C157C2311yescharacteristic
108C4⋊C4×C157C2311yescharacteristic
109C22⋊C4×C157—21no—
110C22⋊C4×C157—21no—
111C22×D157—21no—
112C22×D157C2×D411yescharacteristic
113Dic314—21no—
114Dic314#4112yes—
115D628—21no—
116D628—21no—
117D628—81no—
118C22⋊D157—41no—
119C22⋊D157—42no—
120C22⋊D157—42no—
121C22⋊D157—42no—
122C22⋊D157—81no—
123C22⋊D157—81no—
124C2×Dic157—21no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C2×Dic157—42no—
128C2×Dic157—81no—
129C2×Dic157—81no—
130C2×Dic157C2×D411yescharacteristic
131C2×Dic157C2×D411yescharacteristic
132C2×Dic157C2×D411yescharacteristic
133C4×D157—21no—
134C4×D157—21no—
135C4×D157—42no—
136#11929434—21no—
137#11929434—21no—
138C23×C157—21no—
139C23×C157—21no—
140C23×C157C2×D411yescharacteristic
141D4×C157—21no—
142D4×C157—21no—
143D4×C157—21no—
144D4×C157—21no—
145D4×C157—42no—
146D4×C157—81no—
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×C157—41no—
162C22×C157—41no—
163C22×C157—41no—
164C22×C157C22×D411yescharacteristic
165C2×D157—21no—
166C2×D157—21no—
167C2×D157—21no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C4×C157—21no—
172C4×C157—41no—
173C4×C157—41no—
174C4×C157C2×#4111yescharacteristic
175C4×C157H(5,𝔽2)11yescharacteristic
176Dic157—21no—
177Dic157—22no—
178Dic157—21no—
179Dic157—21no—
180Dic157—41no—
181Dic157—41no—
182C2×C157—41no—
183C2×C157—81no—
184C2×C157—81no—
185C2×C157#54611yescharacteristic
186C2×C157#57511yescharacteristic
187C2×C157#57611yescharacteristic
188D157—41no—
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#469D15711yescharacteristic, complemented
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×D8C2×D15711yescharacteristic
212C2×M16C2×D15711yescharacteristic
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#121C2×D15711yescharacteristic
225#121C2×D15711yescharacteristic
226C4×Q8—1571no—
227C4×D4—3141no—
228C4×D4—3141no—
229C4×D4—1571no—
230C4×D4—1571no—
231#117—1571no—
232C2×C4⋊C4—1571no—
233#107—1571no—
234#107—1571no—
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⋊C8—1571no—
249#97—1571no—
250#41—3142no—
251#41—3142no—
252#41—6281no—
253#41—6281no—
254C2×Q8—1571no—
255C2×D4—21no—
256C2×D4—21no—
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×D4C22×D15711yescharacteristic
266C2×D4C22×D15711yescharacteristic
267C22×C4—3141no—
268C22×C4—3141no—
269C22×C4—3141no—
270C22×C4—3141no—
271C22×C4—1571no—
272C22×C4C22×D15711yescharacteristic
273SD16—3142no—
274D8—41no—
275D8—6281no—
276M16—41no—
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⋊C4—1571no—
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—3141no—
300C42—3141no—
301C42—1571no—
302C23—21no—
303C23—21no—
304C23—3141no—
305C23—1571no—
306C23D4×D15711yescharacteristic
307Q8—3141no—
308Q8—1572no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—81no—
315D4—3141no—
316D4—3141no—
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—3141no—
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—41no—
353C22—41no—
354C22—41no—
355C22—3141no—
356C22—3141no—
357C22—3141no—
358C22—6281no—
359C22—6281no—
360C22—6281no—
361C22C2×D4×D15711yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—3141no—
366C4—3142no—
367C4—3141no—
368C4—3141no—
369C4—6281no—
370C4—6281no—
371C4#41×D15711yescharacteristic
372C4#1909781611yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—6281no—
377C2—12561no—
378C2#2375791211yescharacteristic
379C2#2375806911yescharacteristic
380C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#469×C157C2
socleC22×C157C22×D4
hypercenter#469D157
hypocenterC157#3309
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #23757975C2semidirect
2. #23757941C2semidirect
3. #23757636C2semidirect
4. #23757599C2semidirect
5. #23757584C2semidirect
6. #23757583C2semidirect
7. #23757508C2semidirect
8. #23757466C2semidirect
9. #23757416C2semidirect
10. #23757415C2semidirect
11. #23757370C2semidirect
12. #23757342C2semidirect
13. #23757275C2semidirect
14. #23757266C2semidirect
15. #469×C157C2semidirect
190. C157#3309semidirect
198. #469D157semidirect

Maximal subgroups

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

subgroupindex
#237579752
#237579412
#237576362
#237575992
#237575842
#237575832
#237575082
#237574662
#237574162
#237574152
#237573702
#237573422
#237572752
#237572662
#469×C1572
#3309157