Finite Group Databasebeta

← #16857563

Subgroups — #16857563

Order 3968.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521745C211yesmaximal, characteristic, complemented
2#14521695C211yesmaximal, characteristic, complemented
3#14521404C211yesmaximal, characteristic, complemented
4#14521385C211yesmaximal, characteristic, complemented
5#14521374C211yesmaximal, characteristic, complemented
6#14521350C211yesmaximal, characteristic, complemented
7#14521285C211yesmaximal, characteristic, complemented
8#14521278C211yesmaximal, characteristic, complemented
9#14521265C211yesmaximal, characteristic, complemented
10#14521196C211yesmaximal, characteristic, complemented
11#14521185C211yesmaximal, characteristic, complemented
12C4×D248C211yesmaximal, characteristic, complemented
13#14521046C211yesmaximal, characteristic, complemented
14C2×#11758409C211yesmaximal, characteristic, complemented
15C8×D4×C31C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C22×D124C2211yescharacteristic
18C22×C8×C31C2211yescharacteristic
19C22×C8×C31C2211yescharacteristic, complemented
20C4×D4×C31C2211yescharacteristic
21#11758516—21no—
22#11758514—21no—
23#11758507C2211yescharacteristic
24#11758507C2211yescharacteristic
25#11758507C2211yescharacteristic, complemented
26#11758503C2211yescharacteristic, complemented
27C2×C4⋊Dic31C2211yescharacteristic
28#11758501C2211yescharacteristic
29C2×D248C2211yescharacteristic
30C2×D248C2211yescharacteristic
31C2×#92470C2211yescharacteristic, complemented
32#11758475—21no—
33#11758471—21no—
34#11758461—21no—
35#11758460—21no—
36(C22⋊D31)⋊C4—21no—
37C22⋊C4×D31—21no—
38#11758452C2211yescharacteristic
39C4×D124C2211yescharacteristic
40C4×D124C2211yescharacteristic, complemented
41#11758447C2211yescharacteristic, complemented
42C31×C4⋊C8C2211yescharacteristic, complemented
43C31×C22⋊C8C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic, complemented
45C4×C8×C31C2211yescharacteristic, complemented
46#11758409C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52#11758409C2211yescharacteristic, complemented
53#11758406C2211yescharacteristic, complemented
54#11758406C2211yescharacteristic, complemented
55#11758405C2211yescharacteristic, complemented
56#11758404C2211yescharacteristic, complemented
57#11758404C2211yescharacteristic, complemented
58#11758404C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×D4×C31D411yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C22×Dic31—21no—
68#92495—22no—
69#92495—41no—
70C2×D124—22no—
71C2×D124—21no—
72C2×D124—41no—
73C2×D124C2311yescharacteristic
74C2×D124C2311yescharacteristic
75C2×D124C2311yescharacteristic
76C2×C4×D31—21no—
77C2×C4×D31—21no—
78C2×C4×D31—21no—
79C2×Dic62C2311yescharacteristic
80C2×C8×C31—41no—
81C2×C8×C31—41no—
82C2×C8×C31C2311yescharacteristic
83C2×C8×C31C2311yescharacteristic
84C2×C8×C31C2311yescharacteristic
85C2×C8×C31C2311yescharacteristic
86C4⋊C4×C31D411yescharacteristic
87C22⋊C4×C31D411yescharacteristic
88C22⋊C4×C31D411yescharacteristic
89C42×C31C2311yescharacteristic
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103C4⋊Dic31C2311yescharacteristic
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106Dic31⋊C4—21no—
107C4×Dic31—21no—
108D248—22no—
109D248—41no—
110#92470—41no—
111C23×C31C2×D411yescharacteristic
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31—21no—
115C22×D31—21no—
116C22×D31—42no—
117C22×D31—42no—
118C22×D31—81no—
119D4×C31—22no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2411yescharacteristic
129C22⋊D31—42no—
130C22⋊D31—42no—
131C22⋊D31—81no—
132C22⋊D31—81no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138C2×Dic31—81no—
139D124—21no—
140D124—21no—
141D124—21no—
142D124—21no—
143D124—21no—
144D124—42no—
145D124#4112yes—
146C4×D31—42no—
147C4×D31—81no—
148C4×D31—81no—
149Dic62—21no—
150Dic62—21no—
151C8×C31—21no—
152C8×C31—21no—
153C8×C31—21no—
154C8×C31—21no—
155#3297—311nomaximal, Sylow
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31#13512yes—
162C22×C31C22×D411yescharacteristic
163C2×D31—22no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—41no—
169C2×D31—41no—
170C2×D31—41no—
171C2×D31—41no—
172C2×D31—84no—
173C4×C31—21no—
174C4×C31—21no—
175C4×C31—21no—
176C4×C31—21no—
177C4×C31C2×#4111yescharacteristic
178C4×C31H(5,𝔽2)11yescharacteristic
179Dic31—41no—
180Dic31—41no—
181Dic31—41no—
182Dic31—41no—
183Dic31—41no—
184#553—311no—
185#546—311no—
186#488—311no—
187#484—311no—
188#482—311no—
189#478—311no—
190#466—311no—
191#465—311no—
192#463—311no—
193#449—311no—
194#447—311no—
195C4×D8—311no—
196C8×D4D3111yescharacteristic, complemented
197#416—311no—
198C2×#102—311no—
199C2×C31—22no—
200C2×C31—41no—
201C2×C31#54611yescharacteristic
202C2×C31C2×#13511yescharacteristic
203C2×C31#57611yescharacteristic
204D31—42no—
205D31—81no—
206D31—81no—
207C2×#41—311no—
208C22×D4—311no—
209C2×SD16—311no—
210C2×D8—311no—
211C2×D8—311no—
212C22×C8C2×D3111yescharacteristic
213C22×C8C2×D3111yescharacteristic, complemented
214#126—621no—
215#125—311no—
216#124—311no—
217#123—621no—
218#123—621no—
219C22⋊Q8—311no—
220#121—311no—
221#121—311no—
222#121—311no—
223#121—621no—
224#121—621no—
225#120—621no—
226C4×D4—311no—
227C4×D4—311no—
228C4×D4—621no—
229C4×D4C2×D3111yescharacteristic
230#117—311no—
231C2×C4⋊C4—311no—
232C2×C22⋊C4—621no—
233#107—311no—
234#107—311no—
235#106—311no—
236C4⋊C8C2×D3111yescharacteristic, complemented
237#103—311no—
238#103—311no—
239#103—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246#102—311no—
247C22⋊C8C2×D3111yescharacteristic
248C22⋊C8C2×D3111yescharacteristic, complemented
249C4×C8C2×D3111yescharacteristic, complemented
250C31#329711yescharacteristic, complemented, Sylow
251C24—621no—
252#41—622no—
253#41—1241no—
254C2×Q8—311no—
255C2×D4—311no—
256C2×D4—311no—
257C2×D4—311no—
258C2×D4—622no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4—621no—
262C2×D4—621no—
263C2×D4—621no—
264C2×D4—1241no—
265C2×D4D12411yescharacteristic
266C22×C4—621no—
267C22×C4—621no—
268C22×C4—621no—
269C22×C4—621no—
270C22×C4C22×D3111yescharacteristic
271C22×C4C22×D3111yescharacteristic
272SD16—1241no—
273D8—622no—
274D8—1241no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D3111yescharacteristic
278C2×C8C22×D3111yescharacteristic
279C2×C8C22×D3111yescharacteristic
280C2×C8C22×D3111yescharacteristic
281C4⋊C4—311no—
282C4⋊C4—311no—
283C4⋊C4—311no—
284C4⋊C4—311no—
285C4⋊C4—621no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4—621no—
289C4⋊C4D12411yescharacteristic
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C22⋊C4—621no—
299C22⋊C4D12411yescharacteristic
300C22⋊C4D12411yescharacteristic
301C42—621no—
302C42C22×D3111yescharacteristic
303C23—621no—
304C23—621no—
305C23—621no—
306C23—1242no—
307C23—1242no—
308C23—2481no—
309C23C2×D12411yescharacteristic
310C23C2×D12411yescharacteristic
311Q8—621no—
312Q8—621no—
313D4—22no—
314D4—312no—
315D4—621no—
316D4—621no—
317D4—621no—
318D4—621no—
319D4—621no—
320D4—1242no—
321D4—1242no—
322D4—1242no—
323D4—2481no—
324D4—2481no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—621no—
332C2×C4—621no—
333C2×C4—621no—
334C2×C4—1242no—
335C2×C4—2481no—
336C2×C4—2481no—
337C2×C4—2481no—
338C2×C4C2×D12411yescharacteristic
339C2×C4C2×D12411yescharacteristic
340C2×C4C2×D12411yescharacteristic
341C2×C4C2×D12411yescharacteristic
342C2×C4C23×D3111yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—622no—
353C22—1241no—
354C22—1241no—
355C22—1241no—
356C22—1241no—
357C22—1241no—
358C22—1241no—
359C22—1241no—
360C22—1241no—
361C22—2484no—
362C22#1175848112yes—
363C22C22×D12411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—1241no—
369C4—1241no—
370C4—1241no—
371C4—1241no—
372C4—1241no—
373C4#1175856111yescharacteristic
374C4#41×D3111yescharacteristic
375C2—22no—
376C2—41no—
377C2—1242no—
378C2—2481no—
379C2—2481no—
380C2#1452169411yescharacteristic
381C2C2×#1175848111yescharacteristic
382C2#1452185411yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC8×D4×C31C2
socleC22×C31C22×D4
hypercenterC8×D4D31
hypocenterC31#3297
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14521745C2semidirect
2. #14521695C2semidirect
3. #14521404C2semidirect
4. #14521385C2semidirect
5. #14521374C2semidirect
6. #14521350C2semidirect
7. #14521285C2semidirect
8. #14521278C2semidirect
9. #14521265C2semidirect
10. #14521196C2semidirect
11. #14521185C2semidirect
12. C4×D248C2semidirect
13. #14521046C2semidirect
14. C2×#11758409C2semidirect
15. C8×D4×C31C2semidirect
19. C22×C8×C31C22semidirect
25. #11758507C22semidirect
26. #11758503C22semidirect
31. C2×#92470C22semidirect
40. C4×D124C22semidirect
41. #11758447C22semidirect
42. C31×C4⋊C8C22semidirect
44. C31×C22⋊C8C22semidirect
45. C4×C8×C31C22semidirect
52. #11758409C22semidirect
53. #11758406C22semidirect
54. #11758406C22semidirect
55. #11758405C22semidirect
56. #11758404C22semidirect
57. #11758404C22semidirect
58. #11758404C22semidirect
196. C8×D4D31semidirect
213. C22×C8C2×D31semidirect
236. C4⋊C8C2×D31semidirect
248. C22⋊C8C2×D31semidirect
249. C4×C8C2×D31semidirect
250. C31#3297semidirect

Maximal subgroups

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

subgroupindex
#145217452
#145216952
#145214042
#145213852
#145213742
#145213502
#145212852
#145212782
#145212652
#145211962
#145211852
C4×D2482
#145210462
C2×#117584092
C8×D4×C312
#329731