Finite Group Databasebeta

← #34109590

Subgroups — #34109590

Order 20096.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097794C211yesmaximal, characteristic, complemented
2C2×#19097792C211yesmaximal, characteristic, complemented
3#23757822C211yesmaximal, characteristic, complemented
4C4×#14578955C211yesmaximal, characteristic, complemented
5#23757495C211yesmaximal, characteristic, complemented
6#23757489C211yesmaximal, characteristic, complemented
7#23757485C211yesmaximal, characteristic, complemented
8#23757481C211yesmaximal, characteristic, complemented
9#23757477C211yesmaximal, characteristic, complemented
10#23757471C211yesmaximal, characteristic, complemented
11#23757467C211yesmaximal, characteristic, complemented
12C4⋊C8×D157C211yesmaximal, characteristic, complemented
13#23757268C211yesmaximal, characteristic, complemented
14#23757266C211yesmaximal, characteristic, complemented
15#464×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578955C2211yescharacteristic
18C2×#14578953C2211yescharacteristic
19#19097794—24no—
20#19097792—24no—
21C2×#14578944C2211yescharacteristic
22C2×#14578943C2211yescharacteristic
23C2×#14578941C2211yescharacteristic
24C2×#14578941C2211yescharacteristic
25C2×D1256C2211yescharacteristic
26C2×#14578939C2211yescharacteristic
27C2×C8×D157C2211yescharacteristic
28C2×C8×D157C2211yescharacteristic
29#19097769C2211yescharacteristic
30#19097767C2211yescharacteristic
31#19097759C2211yescharacteristic
32#19097744—21no—
33#19097744—21no—
34Q8×Dic157C2211yescharacteristic
35C4×D628—21no—
36C4×D628C2211yescharacteristic
37#19097733—21no—
38#19097733C2211yescharacteristic
39#19097731—21no—
40#19097731—21no—
41#19097729—21no—
42#19097729C2211yescharacteristic
43C42×D157—21no—
44C42×D157C2211yescharacteristic
45C4⋊#11929434C2211yescharacteristic
46#19097700C2211yescharacteristic
47#19097700C2211yescharacteristic
48#19097696C2211yescharacteristic
49#19097695C2211yescharacteristic
50#19097694C2211yescharacteristic
51#19097693C2211yescharacteristic
52#19097692C2211yescharacteristic
53#19097691C2211yescharacteristic
54C2×Q16×C157C2211yescharacteristic
55C2×SD16×C157C2211yescharacteristic
56#124×C157C2211yescharacteristic
57C4×Q8×C157C2211yescharacteristic
58C4⋊C8×C157C2211yescharacteristic
59#103×C157C2211yescharacteristic
60#102×C157C2211yescharacteristic
61#14578955—22no—
62#14578955—22no—
63#14578955—22no—
64#14578955D414yescomplemented
65#14578953—22no—
66#14578953—22no—
67C2×Dic314C2311yescharacteristic
68C2×D628—21no—
69C2×D628—21no—
70C2×D628C2311yescharacteristic
71C2×D628C2311yescharacteristic
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—
79C2×C4×D157—21no—
80C2×C4×D157D411yescharacteristic
81C2×C4×D157D411yescharacteristic
82C2×C4×D157C2311yescharacteristic
83#14578944—22no—
84#14578943—22no—
85#14578941—22no—
86#14578941—22no—
87D1256—22no—
88#14578939—22no—
89C2×#11929434C2311yescharacteristic
90C2×#11929434C2311yescharacteristic
91C8×D157—22no—
92C8×D157—22no—
93C4⋊Dic157—21no—
94C4⋊Dic157C2311yescharacteristic
95#14578933—21no—
96#14578933—21no—
97#14578931—21no—
98#14578931—21no—
99#14578931—21no—
100#14578931—21no—
101#14578931—21no—
102C4×Dic157—21no—
103C4×Dic157—21no—
104C4×Dic157D411yescharacteristic
105C4×Dic157D411yescharacteristic
106C4×Dic157C2311yescharacteristic
107C2×Q8×C157C2311yescharacteristic
108C2×Q8×C157C2311yescharacteristic
109C2×D4×C157C2311yescharacteristic
110Q16×C157—22no—
111SD16×C157—22no—
112C2×C8×C157C2311yescharacteristic
113C2×C8×C157C2311yescharacteristic
114C4⋊C4×C157—21no—
115C4⋊C4×C157C2311yescharacteristic
116C22⋊C4×C157—21no—
117C22⋊C4×C157—21no—
118C42×C157—21no—
119C42×C157C2311yescharacteristic
120C22×D157—21no—
121C22×D157—21no—
122C22×D157C2×D411yescharacteristic
123Dic314—21no—
124Dic314—21no—
125D628—24no—
126D628—21no—
127D628—21no—
128D628—21no—
129D628—42no—
130D628C2×D412yes—
131C22⋊D157—42no—
132C22⋊D157—42no—
133C22⋊D157—42no—
134C2×Dic157—21no—
135C2×Dic157—21no—
136C2×Dic157—42no—
137C2×Dic157C2×D411yescharacteristic
138C2×Dic157C2×D411yescharacteristic
139C2×Dic157C2×D411yescharacteristic
140C4×D157—24no—
141C4×D157—22no—
142C4×D157—41no—
143C4×D157—42no—
144C4×D157—42no—
145C4×D157—42no—
146C4×D157C2×D412yes—
147C4×D157#4112yes—
148#11929434—21no—
149#11929434—21no—
150C23×C157—21no—
151Q8×C157—21no—
152Q8×C157—21no—
153Q8×C157—21no—
154Q8×C157C2×D412yes—
155D4×C157—21no—
156D4×C157—21no—
157C2×C4×C157—21no—
158C2×C4×C157—21no—
159C2×C4×C157—21no—
160C2×C4×C157C2×D411yescharacteristic
161C2×C4×C157C2×D411yescharacteristic
162C2×C4×C157C2411yescharacteristic
163C8×C157—21no—
164C8×C157—21no—
165C22×C157—41no—
166C22×C157—41no—
167C22×C157—41no—
168C22×C157C22×D411yescharacteristic
169C2×D157—21no—
170C2×D157—21no—
171C2×D157—22no—
172C2×D157—41no—
173C2×D157—41no—
174C2×D157—41no—
175C2×D157—41no—
176C2×D157—41no—
177C2×D157#12112yes—
178C4×C157—22no—
179C4×C157—21no—
180C4×C157—21no—
181C4×C157—41no—
182C4×C157—41no—
183C4×C157C22×D411yescharacteristic
184C4×C157C2×#4111yescharacteristic
185Dic157—21no—
186Dic157—41no—
187Dic157—41no—
188Dic157#12112yes—
189Dic157#13512yescomplemented
190C2×C157—81no—
191C2×C157C2×#12111yescharacteristic
192C2×C157C2×#13511yescharacteristic
193C2×C157#57511yescharacteristic
194D157—22no—
195D157—42no—
196D157—81no—
197C157#303511yescharacteristic, complemented, Sylow
198#3035—1571nomaximal, Sylow
199C2×#135—1571no—
200C2×#135—1571no—
201#532—1571no—
202C4×#41—1571no—
203#464—1571no—
204#464D15711yescharacteristic, complemented
205#463—1571no—
206#463—1571no—
207#462—1571no—
208#461—1571no—
209#460—1571no—
210#459—1571no—
211C2×C4⋊C8—1571no—
212#416—1571no—
213#416—1571no—
214C2×#41—1571no—
215C2×#41—1571no—
216C2×#41—1571no—
217#135—3144no—
218#135—3144no—
219C2×Q16—1571no—
220C2×Q16C2×D15711yescharacteristic
221C2×SD16—1571no—
222C2×SD16—1571no—
223C2×SD16—1571no—
224C2×SD16C2×D15711yescharacteristic
225C2×D8—1571no—
226C2×D8—1571no—
227C22×C8—1571no—
228C22×C8—1571no—
229C4⋊Q8—1571no—
230#127—1571no—
231#124—1571no—
232#124C2×D15711yescharacteristic
233#121—3141no—
234#121—3141no—
235C4×Q8—1571no—
236C4×Q8C2×D15711yescharacteristic
237C4×D4—3141no—
238C4×D4—3141no—
239C4×D4—3141no—
240C4×D4—3141no—
241C4×D4—1571no—
242C4×D4—1571no—
243#117—3141no—
244#117—1571no—
245C2×C42—3141no—
246C2×C42—1571no—
247C4⋊C8—1571no—
248C4⋊C8—1571no—
249C4⋊C8—1571no—
250C4⋊C8C2×D15711yescharacteristic
251#103—1571no—
252#103—1571no—
253#103—1571no—
254#103C2×D15711yescharacteristic
255#102—1571no—
256#102—1571no—
257#102—1571no—
258#102C2×D15711yescharacteristic
259#41—3142no—
260#41—3142no—
261#41—3142no—
262#41—3142no—
263#41—3142no—
264#41—1574no—
265C2×Q8—1571no—
266C2×Q8C22×D15711yescharacteristic
267C2×Q8C22×D15711yescharacteristic
268C2×D4—3141no—
269C2×D4—3141no—
270C2×D4—3141no—
271C2×D4—3141no—
272C2×D4—3141no—
273C2×D4—1571no—
274C2×D4—1571no—
275C2×D4C22×D15711yescharacteristic
276C22×C4—3141no—
277C22×C4—3141no—
278C22×C4—3141no—
279C22×C4—3141no—
280C22×C4—3141no—
281C22×C4—1571no—
282C22×C4—1571no—
283C22×C4—1571no—
284Q16—22no—
285Q16—3142no—
286SD16—22no—
287SD16—3142no—
288SD16—3142no—
289SD16—3142no—
290D8—3142no—
291D8—3142no—
292C2×C8—3142no—
293C2×C8—3142no—
294C2×C8—1571no—
295C2×C8—1571no—
296C2×C8C22×D15711yescharacteristic
297C2×C8C22×D15711yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—3141no—
300C4⋊C4—3141no—
301C4⋊C4—3141no—
302C4⋊C4—1571no—
303C4⋊C4C22×D15711yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—3141no—
307C22⋊C4—3141no—
308C22⋊C4—3141no—
309C22⋊C4—3141no—
310C22⋊C4—3141no—
311C42—21no—
312C42—3141no—
313C42—3141no—
314C42—1571no—
315C42—1571no—
316C42—1571no—
317C42C22×D15711yescharacteristic
318C23—21no—
319C23—3141no—
320C23—3141no—
321C23—1571no—
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—3141no—
326Q8—3141no—
327Q8D4×D15712yes—
328D4—21no—
329D4—21no—
330D4—3144no—
331D4—3141no—
332D4—3141no—
333D4—3141no—
334D4—6282no—
335D4—6282no—
336D4—6282no—
337D4—6282no—
338D4—1572no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3144no—
343C2×C4—3142no—
344C2×C4—3141no—
345C2×C4—3141no—
346C2×C4—6281no—
347C2×C4—6282no—
348C2×C4—6282no—
349C2×C4—6282no—
350C2×C4—6282no—
351C2×C4—1571no—
352C2×C4—1571no—
353C2×C4—1571no—
354C2×C4—1572no—
355C2×C4—1572no—
356C2×C4D4×D15711yescharacteristic
357C2×C4D4×D15711yescharacteristic
358C2×C4C23×D15711yescharacteristic
359C8—21no—
360C8—21no—
361C8—3141no—
362C8—3141no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—3141no—
367C22—3141no—
368C22—3142no—
369C22—6281no—
370C22—6281no—
371C22—6281no—
372C22—6281no—
373C22—6281no—
374C22—1572no—
375C22C2×D4×D15711yescharacteristic
376C4—22no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—3141no—
382C4—6281no—
383C4—6281no—
384C4—1572no—
385C4—1572no—
386C4C2×D4×D15711yescharacteristic
387C4#41×D15711yescharacteristic
388C2—81no—
389C2—3142no—
390C2—6282no—
391C2—12561no—
392C2#121×D15711yescharacteristic
393C2#135×D15711yescharacteristic
394C2#2375807211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#464×C157C2
socleC22×C157C22×D4
hypercenter#464D157
hypocenterC157#3035
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#19097794C2semidirect
2. C2×#19097792C2semidirect
3. #23757822C2semidirect
4. C4×#14578955C2semidirect
5. #23757495C2semidirect
6. #23757489C2semidirect
7. #23757485C2semidirect
8. #23757481C2semidirect
9. #23757477C2semidirect
10. #23757471C2semidirect
11. #23757467C2semidirect
12. C4⋊C8×D157C2semidirect
13. #23757268C2semidirect
14. #23757266C2semidirect
15. #464×C157C2semidirect
64. #14578955D4semidirect
189. Dic157#135semidirect
197. C157#3035semidirect
204. #464D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977942
C2×#190977922
#237578222
C4×#145789552
#237574952
#237574892
#237574852
#237574812
#237574772
#237574712
#237574672
C4⋊C8×D1572
#237572682
#237572662
#464×C1572
#3035157