Finite Group Databasebeta

← #34109587

Subgroups — #34109587

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×#19097791C211yesmaximal, characteristic, complemented
2#23757819C211yesmaximal, characteristic, complemented
3#41×Dic157C211yesmaximal, characteristic, complemented
4#23757497C211yesmaximal, characteristic, complemented
5#23757493C211yesmaximal, characteristic, complemented
6#23757490C211yesmaximal, characteristic, complemented
7#23757486C211yesmaximal, characteristic, complemented
8#23757481C211yesmaximal, characteristic, complemented
9#23757476C211yesmaximal, characteristic, complemented
10#23757471C211yesmaximal, characteristic, complemented
11#23757466C211yesmaximal, characteristic, complemented
12C2×#19097700C211yesmaximal, characteristic, complemented
13#23757270C211yesmaximal, characteristic, complemented
14#23757269C211yesmaximal, characteristic, complemented
15C2×#135×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17#19097791—24no—
18C2×#14578944C2211yescharacteristic
19C2×#14578942C2211yescharacteristic
20C2×#14578941C2211yescharacteristic
21C2×#14578939C2211yescharacteristic
22C22×#11929434C2211yescharacteristic
23#19097769C2211yescharacteristic
24#19097767C2211yescharacteristic
25#19097760C2211yescharacteristic
26#19097758C2211yescharacteristic
27#19097743—21no—
28#19097743—21no—
29Q8×Dic157C2211yescharacteristic
30Q8×Dic157C2211yescharacteristic
31D4×Dic157—21no—
32D4×Dic157—21no—
33D4×Dic157C2211yescharacteristic
34D4×Dic157C2211yescharacteristic
35C4×C22⋊D157—21no—
36C4×C22⋊D157—21no—
37#19097730—21no—
38#19097730C2211yescharacteristic
39C2×C4×Dic157—21no—
40C2×C4×Dic157C2211yescharacteristic
41#19097700C2211yescharacteristic
42#19097700C2211yescharacteristic
43#19097700C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097696C2211yescharacteristic
46#19097696C2211yescharacteristic
47#19097695C2211yescharacteristic
48#19097695C2211yescharacteristic
49#19097693C2211yescharacteristic
50#19097693C2211yescharacteristic
51#19097692C2211yescharacteristic
52#19097692C2211yescharacteristic
53C2×#41×C157C2211yescharacteristic
54C2×#41×C157C2211yescharacteristic
55#135×C157—24no—
56C2×Q16×C157C2211yescharacteristic
57C2×SD16×C157C2211yescharacteristic
58C2×SD16×C157C2211yescharacteristic
59C2×D8×C157C2211yescharacteristic
60C22×C8×C157C2211yescharacteristic
61#14578954—22no—
62#14578954—22no—
63C2×Dic314C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C22×Dic157—21no—
69C22×Dic157—21no—
70C22×Dic157D411yescharacteristic
71C22×Dic157D411yescharacteristic
72C2×C4×D157—21no—
73#14578944—22no—
74#14578942—22no—
75#14578941—22no—
76#14578939—22no—
77C2×#11929434—22no—
78C2×#11929434C2311yescharacteristic
79C2×#11929434C2311yescharacteristic
80C4⋊Dic157—21no—
81C4⋊Dic157—21no—
82C4⋊Dic157C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578933—21no—
86C22⋊Dic157—21no—
87C22⋊Dic157—21no—
88C22⋊Dic157—21no—
89C22⋊Dic157—21no—
90C22⋊Dic157—21no—
91#14578931—21no—
92#14578931—21no—
93C4×Dic157—21no—
94C4×Dic157—21no—
95C4×Dic157—21no—
96C4×Dic157D411yescharacteristic
97C4×Dic157D411yescharacteristic
98C4×Dic157C2311yescharacteristic
99C4×Dic157C2311yescharacteristic
100#41×C157—22no—
101#41×C157—22no—
102#41×C157—22no—
103#41×C157D414yescomplemented
104C2×Q8×C157C2311yescharacteristic
105C2×Q8×C157C2311yescharacteristic
106C2×D4×C157—21no—
107C2×D4×C157—21no—
108C2×D4×C157C2311yescharacteristic
109C2×D4×C157C2311yescharacteristic
110C22×C4×C157—21no—
111C22×C4×C157—21no—
112C22×C4×C157C2311yescharacteristic
113Q16×C157—22no—
114SD16×C157—22no—
115SD16×C157—22no—
116D8×C157—22no—
117C2×C8×C157—22no—
118C2×C8×C157C2311yescharacteristic
119C2×C8×C157C2311yescharacteristic
120C22×D157—21no—
121Dic314—21no—
122Dic314—21no—
123D628—21no—
124D628—21no—
125C22⋊D157—42no—
126C22⋊D157—42no—
127C22⋊D157—42no—
128C2×Dic157—22no—
129C2×Dic157—21no—
130C2×Dic157—21no—
131C2×Dic157—21no—
132C2×Dic157—41no—
133C2×Dic157—42no—
134C2×Dic157—42no—
135C2×Dic157C2×D411yescharacteristic
136C2×Dic157C2×D411yescharacteristic
137C2×Dic157C2×D411yescharacteristic
138C2×Dic157C2×D411yescharacteristic
139C4×D157—42no—
140#11929434—21no—
141#11929434—21no—
142C23×C157—21no—
143C23×C157—21no—
144C23×C157C2×D411yescharacteristic
145Q8×C157—21no—
146Q8×C157—21no—
147Q8×C157—21no—
148Q8×C157C2×D412yes—
149D4×C157—24no—
150D4×C157—21no—
151D4×C157—21no—
152D4×C157—21no—
153D4×C157—42no—
154D4×C157C2×D412yes—
155C2×C4×C157—21no—
156C2×C4×C157—24no—
157C2×C4×C157—21no—
158C2×C4×C157—42no—
159C2×C4×C157C2×D411yescharacteristic
160C2×C4×C157C2×D412yes—
161C2×C4×C157#4112yes—
162C2×C4×C157C2411yescharacteristic
163C8×C157—21no—
164C8×C157—21no—
165C22×C157—21no—
166C22×C157—21no—
167C22×C157—22no—
168C22×C157—41no—
169C22×C157—41no—
170C22×C157—41no—
171C22×C157—41no—
172C22×C157—41no—
173C22×C157#12112yes—
174C22×C157C22×D411yescharacteristic
175C2×D157—41no—
176C2×D157—41no—
177C2×D157—41no—
178C4×C157—22no—
179C4×C157—41no—
180C4×C157#12112yes—
181C4×C157C22×D411yescharacteristic
182C4×C157C2×#4111yescharacteristic
183Dic157—21no—
184Dic157—21no—
185Dic157—21no—
186Dic157—41no—
187Dic157—41no—
188Dic157—41no—
189Dic157#13512yescomplemented
190C2×C157—22no—
191C2×C157—42no—
192C2×C157—81no—
193C2×C157C2×#12111yescharacteristic
194C2×C157C2×#13511yescharacteristic
195C2×C157#57511yescharacteristic
196D157—81no—
197C157#303511yescharacteristic, complemented, Sylow
198#3035—1571nomaximal, Sylow
199C2×#135—1571no—
200C2×#135D15711yescharacteristic, complemented
201#532—1571no—
202C4×#41—1571no—
203#464—1571no—
204#464—1571no—
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×#41C2×D15711yescharacteristic
216C2×#41C2×D15711yescharacteristic
217#135—24no—
218#135—3144no—
219C2×Q16—1571no—
220C2×Q16C2×D15711yescharacteristic
221C2×SD16—1571no—
222C2×SD16—1571no—
223C2×SD16C2×D15711yescharacteristic
224C2×SD16C2×D15711yescharacteristic
225C2×D8—1571no—
226C2×D8C2×D15711yescharacteristic
227C22×C8—1571no—
228C22×C8C2×D15711yescharacteristic
229C4⋊Q8—1571no—
230#127—1571no—
231#124—1571no—
232#124—1571no—
233#121—3141no—
234#121—3141no—
235C4×Q8—1571no—
236C4×Q8—1571no—
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⋊C8—1571no—
251#103—1571no—
252#103—1571no—
253#103—1571no—
254#103—1571no—
255#102—1571no—
256#102—1571no—
257#102—1571no—
258#102—1571no—
259#41—22no—
260#41—22no—
261#41—22no—
262#41—3142no—
263#41—3142no—
264#41C22⋊D15714yescomplemented
265C2×Q8—1571no—
266C2×Q8C22×D15711yescharacteristic
267C2×Q8C22×D15711yescharacteristic
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—3141no—
271C2×D4—3141no—
272C2×D4—3141no—
273C2×D4—1571no—
274C2×D4C22×D15711yescharacteristic
275C2×D4C22×D15711yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—3141no—
279C22×C4—3141no—
280C22×C4—3141no—
281C22×C4—1571no—
282C22×C4—1571no—
283C22×C4C22×D15711yescharacteristic
284Q16—22no—
285Q16—3142no—
286SD16—22no—
287SD16—22no—
288SD16—3142no—
289SD16—3142no—
290D8—22no—
291D8—3142no—
292C2×C8—22no—
293C2×C8—3142no—
294C2×C8—1571no—
295C2×C8—1571no—
296C2×C8C22×D15711yescharacteristic
297C2×C8C22×D15711yescharacteristic
298C4⋊C4—3141no—
299C4⋊C4—3141no—
300C4⋊C4—3141no—
301C4⋊C4—3141no—
302C4⋊C4—1571no—
303C4⋊C4—1571no—
304C22⋊C4—3141no—
305C22⋊C4—3141no—
306C22⋊C4—3141no—
307C22⋊C4—3141no—
308C22⋊C4—3141no—
309C22⋊C4—3141no—
310C22⋊C4—3141no—
311C42—3141no—
312C42—3141no—
313C42—3141no—
314C42—1571no—
315C42—1571no—
316C42—1571no—
317C42—1571no—
318C23—21no—
319C23—21no—
320C23—3141no—
321C23D4×D15711yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—21no—
325Q8—3141no—
326Q8—3141no—
327Q8C2×C22⋊D15712yes—
328D4—24no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—3141no—
334D4—3141no—
335D4—6282no—
336D4—6282no—
337D4—6282no—
338D4C2×C22⋊D15712yes—
339C2×C4—21no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3142no—
344C2×C4—3141no—
345C2×C4—3141no—
346C2×C4—3141no—
347C2×C4—6281no—
348C2×C4—6282no—
349C2×C4—6282no—
350C2×C4—6282no—
351C2×C4—1571no—
352C2×C4—1571no—
353C2×C4—1571no—
354C2×C4—1571no—
355C2×C4D4×D15711yescharacteristic
356C2×C4C2×C22⋊D15712yes—
357C2×C4#1457895312yes—
358C2×C4C23×D15711yescharacteristic
359C8—21no—
360C8—21no—
361C8—3141no—
362C8—3141no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—6281no—
372C22—6281no—
373C22—6281no—
374C22#1909774312yes—
375C22C2×D4×D15711yescharacteristic
376C4—22no—
377C4—41no—
378C4—3141no—
379C4—3141no—
380C4—3141no—
381C4—6281no—
382C4—6281no—
383C4—6281no—
384C4—1572no—
385C4#1909774312yes—
386C4C22×C22⋊D15711yescharacteristic
387C4C2×#1457895311yescharacteristic
388C2—22no—
389C2—42no—
390C2—81no—
391C2—12561no—
392C2C2×#1909774311yescharacteristic
393C2#135×D15711yescharacteristic
394C2#2375807011yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#135×C157C2
socleC22×C157C22×D4
hypercenterC2×#135D157
hypocenterC157#3035
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#19097791C2semidirect
2. #23757819C2semidirect
3. #41×Dic157C2semidirect
4. #23757497C2semidirect
5. #23757493C2semidirect
6. #23757490C2semidirect
7. #23757486C2semidirect
8. #23757481C2semidirect
9. #23757476C2semidirect
10. #23757471C2semidirect
11. #23757466C2semidirect
12. C2×#19097700C2semidirect
13. #23757270C2semidirect
14. #23757269C2semidirect
15. C2×#135×C157C2semidirect
103. #41×C157D4semidirect
189. Dic157#135semidirect
197. C157#3035semidirect
200. C2×#135D157semidirect
264. #41C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977912
#237578192
#41×Dic1572
#237574972
#237574932
#237574902
#237574862
#237574812
#237574762
#237574712
#237574662
C2×#190977002
#237572702
#237572692
C2×#135×C1572
#3035157