Finite Group Databasebeta

← #34102740

Subgroups — #34102740

Order 20096.

484 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×#19097727C211yesmaximal, characteristic
2#23757167C211yesmaximal, characteristic
3#23757166C211yesmaximal, characteristic
4#23757161C211yesmaximal, characteristic
5#23757160C211yesmaximal, characteristic, complemented
6#23757157C211yesmaximal, characteristic, complemented
7#23757155C211yesmaximal, characteristic, complemented
8#23757154C211yesmaximal, characteristic, complemented
9#23757142C211yesmaximal, characteristic, complemented
10#23757137C211yesmaximal, characteristic, complemented
11#23757131C211yesmaximal, characteristic
12#23757131C211yesmaximal, characteristic
13C4×#14578933C211yesmaximal, characteristic, complemented
14#23757124C211yesmaximal, characteristic, complemented
15#388×C157C211yesmaximal, characteristic
16C23×Dic157C2211yescharacteristic
17#19097727C418yescomplemented
18C2×C4⋊Dic157C2211yescharacteristic
19C2×#14578933C2211yescharacteristic
20C2×#14578933C2211yescharacteristic
21C2×#14578933C2211yescharacteristic
22C2×#14578933C2211yescharacteristic
23C2×#14578933C2211yescharacteristic
24C2×#14578933C2211yescharacteristic
25C2×#14578933C2211yescharacteristic
26C2×#14578933C2211yescharacteristic
27C2×C22⋊Dic157C2211yescharacteristic
28C2×C22⋊Dic157C2211yescharacteristic
29C2×C22⋊Dic157C2211yescharacteristic
30C2×C4×Dic157C2211yescharacteristic
31C2×C4×Dic157C2211yescharacteristic
32C2×C4×Dic157C2211yescharacteristic
33C2×C4×Dic157C2211yescharacteristic
34C2×C4×Dic157C2211yescharacteristic
35#19097678C2211yescharacteristic
36#19097678C2211yescharacteristic
37#19097678C2211yescharacteristic
38#19097678C2211yescharacteristic
39#19097678C2211yescharacteristic
40#19097678C2211yescharacteristic
41#19097678C2211yescharacteristic
42#19097678C2211yescharacteristic
43#19097678C2211yescharacteristic
44#19097678C2211yescharacteristic
45C2×C4⋊C4×C157C2211yescharacteristic
46C2×C22⋊C4×C157C2211yescharacteristic
47C2×C22⋊C4×C157C2211yescharacteristic
48C2×C22⋊C4×C157C2211yescharacteristic
49C2×C42×C157C2211yescharacteristic
50#95×C157C2211yescharacteristic
51#95×C157C2211yescharacteristic
52C22×Dic157—22no—
53C22×Dic157—22no—
54C22×Dic157C2×C414yes—
55C22×Dic157C2311yescharacteristic
56C22×Dic157C2311yescharacteristic
57C22×Dic157C2311yescharacteristic
58C22×Dic157C2311yescharacteristic
59C22×Dic157C2311yescharacteristic
60C22×Dic157C2311yescharacteristic
61C22×Dic157C2311yescharacteristic
62C22×Dic157C2311yescharacteristic
63C4⋊Dic157—41no—
64#14578933—22no—
65#14578933—22no—
66#14578933—22no—
67#14578933—22no—
68#14578933—41no—
69#14578933—41no—
70#14578933C2×C414yes—
71#14578933C2×C414yes—
72C22⋊Dic157—41no—
73C22⋊Dic157—41no—
74C22⋊Dic157C2×C414yes—
75C4×Dic157—41no—
76C4×Dic157—41no—
77C4×Dic157—41no—
78C4×Dic157C2×C414yes—
79C4×Dic157C2×C414yes—
80C24×C157C2311yescharacteristic
81C22×C4×C157C2311yescharacteristic
82C22×C4×C157C2311yescharacteristic
83C22×C4×C157C2311yescharacteristic
84C22×C4×C157C2311yescharacteristic
85C22×C4×C157C2311yescharacteristic
86C22×C4×C157C2311yescharacteristic
87C4⋊C4×C157—41no—
88C22⋊C4×C157—41no—
89C22⋊C4×C157—41no—
90C22⋊C4×C157C2×C414yes—
91C42×C157—41no—
92C2×Dic157—21no—
93C2×Dic157—21no—
94C2×Dic157—21no—
95C2×Dic157—21no—
96C2×Dic157—21no—
97C2×Dic157—21no—
98C2×Dic157—28no—
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×Dic157C22×C412yes—
112C2×Dic157C22×C412yes—
113C2×Dic157C22×C412yes—
114C2×Dic157C22×C412yes—
115C2×Dic157#4112yes—
116C2×Dic157#4112yes—
117C23×C157—21no—
118C23×C157—21no—
119C23×C157—21no—
120C23×C157—21no—
121C23×C157—21no—
122C23×C157—21no—
123C23×C157C22×C412yes—
124C23×C157C2411yescharacteristic
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×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157C22×C412yes—
142C2×C4×C157C22×C412yes—
143C22×C157—22no—
144C22×C157—22no—
145C22×C157—22no—
146C22×C157—41no—
147C22×C157—41no—
148C22×C157—41no—
149C22×C157—41no—
150C22×C157C23×C411yescharacteristic
151C22×C157C2×#4111yescharacteristic
152C22×C157C2×#4111yescharacteristic
153C22×C157H(5,𝔽2)11yescharacteristic
154C22×C157H(5,𝔽2)11yescharacteristic
155C22×C1572−1+411yescharacteristic
156C22×C1572−1+411yescharacteristic
157C4×C157—22no—
158C4×C157—22no—
159C4×C157—41no—
160C4×C157—41no—
161C4×C157—41no—
162C4×C157—41no—
163Dic157—22no—
164Dic157—22no—
165Dic157—22no—
166Dic157—41no—
167Dic157—41no—
168Dic157—41no—
169Dic157—41no—
170Dic157#11714yes—
171C2×C157—42no—
172C2×C157C2×#11711yescharacteristic
173C2×C157#52011yescharacteristic
174C2×C157#52011yescharacteristic
175C2×C157#54011yescharacteristic
176C2×C157#54111yescharacteristic
177C2×C157#54211yescharacteristic
178C2×C157#54211yescharacteristic
179C157#231411yescharacteristic, complemented, Sylow
180#2314—1571nomaximal, Sylow
181C2×#117—1571no—
182#388—1571no—
183#388—1571no—
184#388—1571no—
185#388D15711yescharacteristic
186#387—1571no—
187#387—1571no—
188#387—1571no—
189#387—1571no—
190#384—1571no—
191#382—1571no—
192#380—1571no—
193#380—1571no—
194C4×C4⋊C4—1571no—
195C4×C4⋊C4—1571no—
196C23×C4—1571no—
197#117—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⋊C4—1571no—
205C2×C4⋊C4—1571no—
206C2×C4⋊C4—1571no—
207C2×C4⋊C4C2×D15711yescharacteristic
208C2×C22⋊C4—1571no—
209C2×C22⋊C4—1571no—
210C2×C22⋊C4—1571no—
211C2×C22⋊C4C2×D15711yescharacteristic
212C2×C22⋊C4C2×D15711yescharacteristic
213C2×C22⋊C4C2×D15711yescharacteristic
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#95—1571no—
229#95—1571no—
230#95C2×D15711yescharacteristic
231#95C2×D15711yescharacteristic
232C24C22×D15711yescharacteristic
233C22×C4—3142no—
234C22×C4—3142no—
235C22×C4—1571no—
236C22×C4—1571no—
237C22×C4—1571no—
238C22×C4—1571no—
239C22×C4—1574no—
240C22×C4—1571no—
241C22×C4—1571no—
242C22×C4—1571no—
243C22×C4—1571no—
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—6281no—
256C4⋊C4—6281no—
257C4⋊C4—6281no—
258C4⋊C4—1574no—
259C4⋊C4—1574no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—6281no—
263C22⋊C4—6281no—
264C22⋊C4—1574no—
265C22⋊C4C4×D15714yes—
266C42—41no—
267C42—6281no—
268C42—6281no—
269C42—6281no—
270C42—1574no—
271C42—1574no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D15712yes—
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—3141no—
297C2×C4—3141no—
298C2×C4—3141no—
299C2×C4—3141no—
300C2×C4—3141no—
301C2×C4—3141no—
302C2×C4—3148no—
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—3141no—
313C2×C4—3141no—
314C2×C4—3141no—
315C2×C4—1572no—
316C2×C4—1572no—
317C2×C4—1572no—
318C2×C4—1572no—
319C2×C4—1572no—
320C2×C4—1572no—
321C2×C4C2×C4×D15712yes—
322C2×C4C2×C4×D15712yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D15711yescharacteristic
331C22#41×D15711yescharacteristic
332C22#41×D15711yescharacteristic
333C22#1909781611yescharacteristic
334C22#1909781611yescharacteristic
335C22#1909781811yescharacteristic
336C22#1909781811yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3142no—
344C4—3142no—
345C4—3142no—
346C4—6281no—
347C4—6281no—
348C4—6281no—
349C4—6281no—
350C4—1574no—
351C2—42no—
352C2#117×D15711yescharacteristic
353C2#2375775211yescharacteristic
354C2#2375775211yescharacteristic
355C2#2375787311yescharacteristic
356C2#2375788011yescharacteristic
357C2#2375788711yescharacteristic
358C2#2375789111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutatorC22×C157C23×C4
Fitting#388×C157C2
socle, cosocleC23×C157C24
prime radicalC24×C157C23
hypercenter#388D157
hypocenterC157#2314
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
5. #23757160C2semidirect
6. #23757157C2semidirect
7. #23757155C2semidirect
8. #23757154C2semidirect
9. #23757142C2semidirect
10. #23757137C2semidirect
13. C4×#14578933C2semidirect
14. #23757124C2semidirect
17. #19097727C4semidirect
179. C157#2314semidirect

Maximal subgroups

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

subgroupindex
C2×#190977272
#237571672
#237571662
#237571612
#237571602
#237571572
#237571552
#237571542
#237571422
#237571372
#237571312
C4×#145789332
#237571242
#388×C1572
#2314157