Finite Group Databasebeta

← #34111686

Subgroups — #34111686

Order 20096.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097803C211yesmaximal, characteristic, complemented
2C2×#19097794C211yesmaximal, characteristic, complemented
3#23757935C211yesmaximal, characteristic, complemented
4#23757926C211yesmaximal, characteristic, complemented
5#23757665C211yesmaximal, characteristic, complemented
6#23757522C211yesmaximal, characteristic, complemented
7#23757513C211yesmaximal, characteristic, complemented
8#23757489C211yesmaximal, characteristic, complemented
9#23757438C211yesmaximal, characteristic, complemented
10#23757434C211yesmaximal, characteristic, complemented
11#23757427C211yesmaximal, characteristic, complemented
12#23757421C211yesmaximal, characteristic, complemented
13#23757371C211yesmaximal, characteristic, complemented
14#23757343C211yesmaximal, characteristic, complemented
15#462×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578955C2211yescharacteristic
18C2×#14578955C2211yescharacteristic
19C2×Q8×D157C2211yescharacteristic
20#19097803—24no—
21#19097794—24no—
22C2×#14578944C2211yescharacteristic
23C2×#14578944C2211yescharacteristic
24C2×#14578943C2211yescharacteristic
25C2×#14578941C2211yescharacteristic
26C2×#14578941C2211yescharacteristic
27C2×#14578941C2211yescharacteristic
28C2×D1256C2211yescharacteristic
29C2×#14578937C2211yescharacteristic
30C2×C8×D157C2211yescharacteristic
31#19097759—21no—
32#19097759C2211yescharacteristic
33#19097756—21no—
34#19097756—21no—
35#19097751—21no—
36#19097751C2211yescharacteristic
37#19097747C2211yescharacteristic
38#19097747C2211yescharacteristic
39#19097746—21no—
40#19097746—21no—
41#19097746C2211yescharacteristic
42C4×D628—21no—
43C4×D628C2211yescharacteristic
44C4×D628C2211yescharacteristic
45C4⋊C4×D157—21no—
46#19097704C2211yescharacteristic
47#19097696C2211yescharacteristic
48#19097695C2211yescharacteristic
49#19097693C2211yescharacteristic
50#19097691C2211yescharacteristic
51#19097683C2211yescharacteristic
52#19097683C2211yescharacteristic
53#19097682C2211yescharacteristic
54C2×Q16×C157C2211yescharacteristic
55C2×Q16×C157C2211yescharacteristic
56C4⋊Q8×C157C2211yescharacteristic
57C4×Q8×C157C2211yescharacteristic
58C4⋊C8×C157C2211yescharacteristic
59#103×C157C2211yescharacteristic
60#103×C157C2211yescharacteristic
61#14578955—22no—
62#14578955—22no—
63#14578955—22no—
64#14578955—41no—
65#14578955—41no—
66#14578955—41no—
67C2×Dic314—21no—
68C2×Dic314C2311yescharacteristic
69Q8×D157—22no—
70Q8×D157—41no—
71C2×D628—21no—
72C2×D628—21no—
73C2×D628—21no—
74C2×D628—21no—
75C2×D628D411yescharacteristic
76C2×D628C2311yescharacteristic
77C2×D628C2311yescharacteristic
78C2×C4×D157—21no—
79C2×C4×D157—21no—
80C2×C4×D157—21no—
81C2×C4×D157—21no—
82C2×C4×D157—21no—
83C2×C4×D157C2311yescharacteristic
84C2×C4×D157C2311yescharacteristic
85#14578944—22no—
86#14578944—41no—
87#14578943—22no—
88#14578941—22no—
89#14578941—41no—
90#14578941D414yescomplemented
91D1256—22no—
92#14578937—22no—
93C2×#11929434C2311yescharacteristic
94C2×#11929434C2311yescharacteristic
95C8×D157—22no—
96C4⋊Dic157—21no—
97C4⋊Dic157D411yescharacteristic
98C4⋊Dic157C2311yescharacteristic
99#14578933—21no—
100#14578933—21no—
101#14578931—21no—
102#14578931—21no—
103#14578931—21no—
104#14578931—21no—
105#14578931—21no—
106#14578931—21no—
107#14578931—21no—
108#14578931D411yescharacteristic
109#14578931D411yescharacteristic
110C2×Q8×C157C2311yescharacteristic
111C2×Q8×C157C2311yescharacteristic
112C2×Q8×C157C2311yescharacteristic
113Q16×C157—22no—
114Q16×C157—22no—
115C2×C8×C157C2311yescharacteristic
116C2×C8×C157C2311yescharacteristic
117C4⋊C4×C157—21no—
118C4⋊C4×C157—21no—
119C4⋊C4×C157—21no—
120C4⋊C4×C157C2311yescharacteristic
121C42×C157—21no—
122C42×C157C2311yescharacteristic
123C22×D157—21no—
124C22×D157—21no—
125C22×D157C2×D411yescharacteristic
126C22×D157C2×D411yescharacteristic
127Dic314—21no—
128Dic314—21no—
129Dic314—42no—
130D628—21no—
131D628—21no—
132D628—21no—
133D628—41no—
134D628—42no—
135D628—42no—
136D628—42no—
137D628—42no—
138D628C2×D412yes—
139C2×Dic157—21no—
140C2×Dic157—21no—
141C2×Dic157C2×D411yescharacteristic
142C2×Dic157C2×D411yescharacteristic
143C4×D157—21no—
144C4×D157—21no—
145C4×D157—21no—
146C4×D157—21no—
147C4×D157—42no—
148C4×D157—42no—
149C4×D157—42no—
150C4×D157—42no—
151C4×D157—42no—
152#11929434—21no—
153#11929434C2×D412yes—
154Q8×C157—21no—
155Q8×C157—21no—
156Q8×C157—21no—
157Q8×C157—21no—
158Q8×C157—21no—
159Q8×C157C2×D412yes—
160C2×C4×C157—21no—
161C2×C4×C157—21no—
162C2×C4×C157—21no—
163C2×C4×C157—21no—
164C2×C4×C157C2×D411yescharacteristic
165C2×C4×C157C2×D411yescharacteristic
166C2×C4×C157C2411yescharacteristic
167C8×C157—21no—
168C8×C157—21no—
169C22×C157C22×D411yescharacteristic
170C2×D157—21no—
171C2×D157—21no—
172C2×D157—22no—
173C2×D157—21no—
174C2×D157—21no—
175C2×D157—21no—
176C2×D157—21no—
177C2×D157—41no—
178C2×D157—41no—
179C2×D157—41no—
180C2×D157—41no—
181C2×D157—41no—
182C4×C157—22no—
183C4×C157—21no—
184C4×C157—21no—
185C4×C157—41no—
186C4×C157—41no—
187C4×C157—41no—
188C4×C157C22×D411yescharacteristic
189C4×C157H(5,𝔽2)11yescharacteristic
190Dic157—21no—
191Dic157—21no—
192Dic157—41no—
193Dic157—41no—
194C2×C157D4211yescharacteristic
195C2×C157#57511yescharacteristic
196C2×C157#57811yescharacteristic
197D157—41no—
198D157—41no—
199D157—42no—
200D157—81no—
201C157#326911yescharacteristic, complemented, Sylow
202#3269—1571nomaximal, Sylow
203C2×#137—1571no—
204C2×#135—1571no—
205#548—1571no—
206#547—1571no—
207#497—1571no—
208#468—1571no—
209#467—1571no—
210#463—1571no—
211#462D15711yescharacteristic, complemented
212#452—1571no—
213#452—1571no—
214#451—1571no—
215#449—1571no—
216#440—1571no—
217#435—1571no—
218C2×#41—1571no—
219C2×#41—1571no—
220C2×#41—1571no—
221C22×Q8—1571no—
222#137—3144no—
223#135—3144no—
224C2×Q16—1571no—
225C2×Q16—1571no—
226C2×Q16C2×D15711yescharacteristic
227C2×Q16C2×D15711yescharacteristic
228C2×SD16—1571no—
229C2×SD16—1571no—
230C2×SD16—1571no—
231C2×SD16—1571no—
232C2×D8—1571no—
233C2×M16—1571no—
234C22×C8—1571no—
235C4⋊Q8C2×D15711yescharacteristic
236#124—3141no—
237#124—1571no—
238#123—3141no—
239#123—3141no—
240C22⋊Q8—3141no—
241C22⋊Q8—1571no—
242C22⋊Q8—1571no—
243C22⋊Q8—1571no—
244#121—3141no—
245#121—3141no—
246#121—1571no—
247C4×Q8C2×D15711yescharacteristic
248C4×D4—3141no—
249C4×D4—1571no—
250C4×D4—1571no—
251C2×C4⋊C4—3141no—
252#107—1571no—
253C4⋊C8C2×D15711yescharacteristic
254#103—1571no—
255#103—1571no—
256#103C2×D15711yescharacteristic
257#103C2×D15711yescharacteristic
258#102—1571no—
259#102—1571no—
260C22⋊C8—1571no—
261C22⋊C8—1571no—
262#97—1571no—
263#41—3142no—
264#41—3142no—
265#41—3142no—
266#41—6281no—
267#41—6281no—
268#41—6281no—
269C2×Q8—3141no—
270C2×Q8—3142no—
271C2×Q8—6281no—
272C2×Q8—1571no—
273C2×Q8C22×D15711yescharacteristic
274C2×Q8C22×D15711yescharacteristic
275C2×Q8C22×D15711yescharacteristic
276C2×D4—3141no—
277C2×D4—3141no—
278C2×D4—3141no—
279C2×D4—3141no—
280C2×D4—1571no—
281C2×D4—1571no—
282C2×D4—1571no—
283C22×C4—3141no—
284C22×C4—3141no—
285C22×C4—3141no—
286C22×C4—3141no—
287C22×C4—3141no—
288C22×C4—1571no—
289C22×C4—1571no—
290Q16—22no—
291Q16—22no—
292Q16—3142no—
293Q16—6281no—
294SD16—3142no—
295SD16—3142no—
296SD16—6281no—
297SD16—1574no—
298D8—3142no—
299M16—3142no—
300C2×C8—3142no—
301C2×C8—1571no—
302C2×C8—1571no—
303C2×C8C22×D15711yescharacteristic
304C2×C8C22×D15711yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—3141no—
309C4⋊C4—3141no—
310C4⋊C4—3141no—
311C4⋊C4—1571no—
312C4⋊C4—1571no—
313C4⋊C4C22×D15711yescharacteristic
314C22⋊C4—3141no—
315C22⋊C4—3141no—
316C22⋊C4—3141no—
317C22⋊C4—3141no—
318C22⋊C4—3141no—
319C22⋊C4—3141no—
320C22⋊C4—3141no—
321C22⋊C4—1571no—
322C22⋊C4—1571no—
323C42—21no—
324C42C22×D15711yescharacteristic
325C23—3141no—
326C23—3141no—
327C23—1571no—
328C23—1571no—
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—3141no—
335Q8—3141no—
336Q8—6282no—
337Q8D4×D15712yes—
338D4—3141no—
339D4—3141no—
340D4—3141no—
341D4—6281no—
342D4—6282no—
343D4—6282no—
344D4—6282no—
345D4—6282no—
346D4—1572no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3141no—
352C2×C4—3141no—
353C2×C4—3141no—
354C2×C4—3141no—
355C2×C4—3141no—
356C2×C4—3141no—
357C2×C4—6282no—
358C2×C4—6282no—
359C2×C4—6282no—
360C2×C4—6282no—
361C2×C4—6282no—
362C2×C4—1571no—
363C2×C4—1571no—
364C2×C4D4×D15711yescharacteristic
365C2×C4D4×D15711yescharacteristic
366C2×C4C23×D15711yescharacteristic
367C8—21no—
368C8—21no—
369C8—3141no—
370C8—1572no—
371C22—3141no—
372C22—3141no—
373C22—3141no—
374C22—3141no—
375C22—3142no—
376C22—3141no—
377C22—3141no—
378C22—6281no—
379C22—6281no—
380C22—6281no—
381C22—6281no—
382C22—6281no—
383C22C2×D4×D15711yescharacteristic
384C4—21no—
385C4—22no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—3141no—
391C4—3141no—
392C4—6281no—
393C4—6281no—
394C4C2×D4×D15711yescharacteristic
395C4#1909781711yescharacteristic
396C2—6281no—
397C2—6281no—
398C2—6282no—
399C2—12561no—
400C2#2375790711yescharacteristic
401C2#2375807211yescharacteristic
402C2#2375808611yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#462×C157C2
socleC22×C157C22×D4
hypercenter#462D157
hypocenterC157#3269
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. C2×#19097803C2semidirect
2. C2×#19097794C2semidirect
3. #23757935C2semidirect
4. #23757926C2semidirect
5. #23757665C2semidirect
6. #23757522C2semidirect
7. #23757513C2semidirect
8. #23757489C2semidirect
9. #23757438C2semidirect
10. #23757434C2semidirect
11. #23757427C2semidirect
12. #23757421C2semidirect
13. #23757371C2semidirect
14. #23757343C2semidirect
15. #462×C157C2semidirect
90. #14578941D4semidirect
201. C157#3269semidirect
211. #462D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190978032
C2×#190977942
#237579352
#237579262
#237576652
#237575222
#237575132
#237574892
#237574382
#237574342
#237574272
#237574212
#237573712
#237573432
#462×C1572
#3269157