Finite Group Databasebeta

← #34103262

Subgroups — #34103262

Order 20096.

496 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097766C211yesmaximal, characteristic
2#23757169C211yesmaximal, characteristic, complemented
3#23757163C211yesmaximal, characteristic
4#23757162C211yesmaximal, characteristic
5#23757162C211yesmaximal, characteristic
6#23757160C211yesmaximal, characteristic, complemented
7#23757158C211yesmaximal, characteristic, complemented
8#23757147C211yesmaximal, characteristic
9C4⋊C4×Dic157C211yesmaximal, characteristic, complemented
10C4×#14578933C211yesmaximal, characteristic, complemented
11#23757124C211yesmaximal, characteristic, complemented
12C4×#14578931C211yesmaximal, characteristic
13#23757120C211yesmaximal, characteristic
14#23757118C211yesmaximal, characteristic, complemented
15#387×C157C211yesmaximal, characteristic, complemented
16C22×C4×D157C2211yescharacteristic
17#19097766C418yescomplemented
18C2×C4⋊Dic157C2211yescharacteristic
19C2×C4⋊Dic157C2211yescharacteristic
20C2×#14578933C2211yescharacteristic
21C2×#14578933C2211yescharacteristic
22C2×#14578933C2211yescharacteristic
23C2×#14578933C2211yescharacteristic
24C2×#14578931C2211yescharacteristic
25C2×#14578931C2211yescharacteristic
26C2×#14578931C2211yescharacteristic
27C2×#14578931C2211yescharacteristic
28C2×#14578931C2211yescharacteristic
29C2×#14578931C2211yescharacteristic
30C2×C4×Dic157C2211yescharacteristic
31C2×C4×Dic157C2211yescharacteristic
32C2×C4×Dic157C2211yescharacteristic
33C2×C4×Dic157C2211yescharacteristic
34C2×C4×Dic157C2211yescharacteristic
35C2×C4×Dic157C2211yescharacteristic
36C2×C4×Dic157C2211yescharacteristic
37#19097678C2211yescharacteristic
38#19097678C2211yescharacteristic
39#19097678C2211yescharacteristic
40#19097678C2211yescharacteristic
41#19097678C2211yescharacteristic
42#19097678C2211yescharacteristic
43#19097678C2211yescharacteristic
44#19097678C2211yescharacteristic
45C2×C4⋊C4×C157C2211yescharacteristic
46C2×C4⋊C4×C157C2211yescharacteristic
47C2×C42×C157C2211yescharacteristic
48#95×C157C2211yescharacteristic
49#95×C157C2211yescharacteristic
50#95×C157C2211yescharacteristic
51#95×C157C2211yescharacteristic
52C23×D157C2311yescharacteristic
53C22×Dic157C2311yescharacteristic
54C22×Dic157C2311yescharacteristic
55C22×Dic157C2311yescharacteristic
56C22×Dic157C2311yescharacteristic
57C22×Dic157C2311yescharacteristic
58C22×Dic157C2311yescharacteristic
59C22×Dic157C2311yescharacteristic
60C2×C4×D157—22no—
61C2×C4×D157—22no—
62C2×C4×D157—41no—
63C4⋊Dic157—22no—
64C4⋊Dic157C2×C414yescomplemented
65#14578933—22no—
66#14578933—22no—
67#14578933—22no—
68#14578933C2×C414yescomplemented
69#14578931—22no—
70#14578931—22no—
71#14578931—41no—
72#14578931C2×C414yes—
73#14578931C2×C414yes—
74#14578931C2×C414yes—
75C4×Dic157—22no—
76C4×Dic157—22no—
77C4×Dic157—22no—
78C4×Dic157—22no—
79C4×Dic157—41no—
80C4×Dic157—41no—
81C4×Dic157C2×C414yescomplemented
82C22×C4×C157C2311yescharacteristic
83C22×C4×C157C2311yescharacteristic
84C22×C4×C157C2311yescharacteristic
85C22×C4×C157C2311yescharacteristic
86C22×C4×C157C2311yescharacteristic
87C22×C4×C157C2311yescharacteristic
88C22×C4×C157C2311yescharacteristic
89C4⋊C4×C157—41no—
90C4⋊C4×C157C2×C414yescomplemented
91C42×C157—41no—
92C22×D157—21no—
93C22×D157—21no—
94C22×D157—21no—
95C22×D157—21no—
96C22×D157—21no—
97C22×D157—21no—
98C22×D157C22×C412yes—
99C2×Dic157—21no—
100C2×Dic157—21no—
101C2×Dic157—21no—
102C2×Dic157—21no—
103C2×Dic157—21no—
104C2×Dic157—21no—
105C2×Dic157—21no—
106C2×Dic157—21no—
107C2×Dic157—21no—
108C2×Dic157—21no—
109C2×Dic157—21no—
110C2×Dic157—21no—
111C2×Dic157—21no—
112C2×Dic157—21no—
113C2×Dic157—21no—
114C2×Dic157C22×C412yes—
115C2×Dic157C22×C412yes—
116C2×Dic157C22×C412yes—
117C2×Dic157#4112yes—
118C2×Dic157#4112yes—
119C2×Dic157#4112yes—
120C4×D157—44no—
121C23×C157C2411yescharacteristic
122C2×C4×C157—21no—
123C2×C4×C157—21no—
124C2×C4×C157—21no—
125C2×C4×C157—21no—
126C2×C4×C157—21no—
127C2×C4×C157—21no—
128C2×C4×C157—21no—
129C2×C4×C157—21no—
130C2×C4×C157—21no—
131C2×C4×C157—21no—
132C2×C4×C157—21no—
133C2×C4×C157—21no—
134C2×C4×C157—21no—
135C2×C4×C157—21no—
136C2×C4×C157—21no—
137C2×C4×C157—21no—
138C2×C4×C157—21no—
139C2×C4×C157C22×C412yes—
140C2×C4×C157C22×C412yes—
141C2×C4×C157C22×C412yes—
142C2×C4×C157#4112yes—
143C22×C157C23×C411yescharacteristic
144C22×C157C2×#4111yescharacteristic
145C22×C157C2×#4111yescharacteristic
146C22×C157C2×#4111yescharacteristic
147C22×C157C2×#4111yescharacteristic
148C22×C157H(5,𝔽2)11yescharacteristic
149C22×C1572−1+411yescharacteristic
150C2×D157—22no—
151C2×D157—22no—
152C2×D157—22no—
153C2×D157—41no—
154C2×D157—41no—
155C2×D157—41no—
156C2×D157—41no—
157C4×C157—22no—
158C4×C157—22no—
159C4×C157—22no—
160C4×C157—22no—
161C4×C157—41no—
162C4×C157—41no—
163C4×C157—41no—
164Dic157—22no—
165Dic157—22no—
166Dic157—22no—
167Dic157—22no—
168Dic157—22no—
169Dic157—22no—
170Dic157—41no—
171C2×C157C4×#4111yescharacteristic
172C2×C157C4×#4111yescharacteristic
173C2×C157#52011yescharacteristic
174C2×C157#55111yescharacteristic
175C2×C157#55211yescharacteristic
176C2×C157#55311yescharacteristic
177C2×C157#55611yescharacteristic
178D157—42no—
179C157#237311yescharacteristic, complemented, Sylow
180#2373—1571nomaximal, Sylow
181C2×#126—1571no—
182#389—1571no—
183#388—1571no—
184#388—1571no—
185#388—1571no—
186#387—1571no—
187#387—1571no—
188#387D15711yescharacteristic, complemented
189#385—1571no—
190C4×C4⋊C4—1571no—
191C4×C4⋊C4—1571no—
192C4×C4⋊C4—1571no—
193C4×C22⋊C4—1571no—
194C4×C22⋊C4—1571no—
195#376—1571no—
196C23×C4—1571no—
197#126—1578no—
198C2×C4⋊C4—1571no—
199C2×C4⋊C4—1571no—
200C2×C4⋊C4—1571no—
201C2×C4⋊C4—1571no—
202C2×C4⋊C4—1571no—
203C2×C4⋊C4—1571no—
204C2×C4⋊C4C2×D15711yescharacteristic
205C2×C4⋊C4C2×D15711yescharacteristic
206C2×C22⋊C4—1571no—
207C2×C22⋊C4—1571no—
208C2×C22⋊C4—1571no—
209C2×C22⋊C4—1571no—
210C2×C22⋊C4—1571no—
211C2×C22⋊C4—1571no—
212C2×C42—1571no—
213C2×C42—1571no—
214C2×C42—1571no—
215C2×C42—1571no—
216C2×C42—1571no—
217C2×C42—1571no—
218C2×C42—1571no—
219C2×C42C2×D15711yescharacteristic
220#95—1571no—
221#95—1571no—
222#95—1571no—
223#95—1571no—
224#95—1571no—
225#95—1571no—
226#95—1571no—
227#95—1571no—
228#95C2×D15711yescharacteristic
229#95C2×D15711yescharacteristic
230#95C2×D15711yescharacteristic
231#95C2×D15711yescharacteristic
232C24—1571no—
233C22×C4—3142no—
234C22×C4—3142no—
235C22×C4—6281no—
236C22×C4—1571no—
237C22×C4—1571no—
238C22×C4—1571no—
239C22×C4—1571no—
240C22×C4—1571no—
241C22×C4—1571no—
242C22×C4—1571no—
243C22×C4C22×D15711yescharacteristic
244C22×C4C22×D15711yescharacteristic
245C22×C4C22×D15711yescharacteristic
246C22×C4C22×D15711yescharacteristic
247C22×C4C22×D15711yescharacteristic
248C22×C4C22×D15711yescharacteristic
249C22×C4C22×D15711yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—3142no—
252C4⋊C4—3142no—
253C4⋊C4—3142no—
254C4⋊C4—3142no—
255C4⋊C4—1574no—
256C4⋊C4—1574no—
257C4⋊C4C4×D15714yescomplemented
258C22⋊C4—3142no—
259C22⋊C4—3142no—
260C22⋊C4—6281no—
261C22⋊C4—1574no—
262C22⋊C4—1574no—
263C22⋊C4—1574no—
264C42—41no—
265C42—3142no—
266C42—3142no—
267C42—3142no—
268C42—3142no—
269C42—6281no—
270C42—6281no—
271C42—1574no—
272C23—3141no—
273C23—3141no—
274C23—3141no—
275C23—3141no—
276C23—3141no—
277C23—3141no—
278C23—1572no—
279C23C23×D15711yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—3141no—
298C2×C4—3141no—
299C2×C4—3141no—
300C2×C4—3141no—
301C2×C4—3141no—
302C2×C4—3141no—
303C2×C4—3141no—
304C2×C4—3141no—
305C2×C4—3141no—
306C2×C4—3141no—
307C2×C4—3141no—
308C2×C4—3141no—
309C2×C4—3141no—
310C2×C4—3141no—
311C2×C4—3141no—
312C2×C4—6284no—
313C2×C4—1572no—
314C2×C4—1572no—
315C2×C4—1572no—
316C2×C4—1572no—
317C2×C4—1572no—
318C2×C4—1572no—
319C2×C4C2×C4×D15712yes—
320C2×C4C2×C4×D15712yes—
321C2×C4C2×C4×D15712yes—
322C2×C4#1457895512yes—
323C22—3142no—
324C22—3142no—
325C22—3142no—
326C22—6281no—
327C22—6281no—
328C22—6281no—
329C22—6281no—
330C22C22×C4×D15711yescharacteristic
331C22#41×D15711yescharacteristic
332C22#41×D15711yescharacteristic
333C22#41×D15711yescharacteristic
334C22C2×#1457895511yescharacteristic
335C22#1909781611yescharacteristic
336C22#1909781811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—3142no—
345C4—3142no—
346C4—3142no—
347C4—3142no—
348C4—3142no—
349C4—3142no—
350C4—6281no—
351C2—6282no—
352C2#2375774111yescharacteristic
353C2C4×#1457895511yescharacteristic
354C2#2375775211yescharacteristic
355C2#2375795011yescharacteristic
356C2#2375796111yescharacteristic
357C2#2375796811yescharacteristic
358C2#2375799011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#387×C157C2
socle, cosocleC23×C157C24
prime radicalC23×D157C23
hypercenter#387D157
hypocenterC157#2373
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #23757169C2semidirect
6. #23757160C2semidirect
7. #23757158C2semidirect
9. C4⋊C4×Dic157C2semidirect
10. C4×#14578933C2semidirect
11. #23757124C2semidirect
14. #23757118C2semidirect
15. #387×C157C2semidirect
17. #19097766C4semidirect
64. C4⋊Dic157C2×C4semidirect
68. #14578933C2×C4semidirect
81. C4×Dic157C2×C4semidirect
90. C4⋊C4×C157C2×C4semidirect
179. C157#2373semidirect
188. #387D157semidirect
257. C4⋊C4C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977662
#237571692
#237571632
#237571622
#237571602
#237571582
#237571472
C4⋊C4×Dic1572
C4×#145789332
#237571242
C4×#145789312
#237571202
#237571182
#387×C1572
#2373157