Finite Group Databasebeta

← #16857550

Subgroups — #16857550

Order 3968.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521741C211yesmaximal, characteristic, complemented
2#14521693C211yesmaximal, characteristic
3#14521402C211yesmaximal, characteristic, complemented
4#14521380C211yesmaximal, characteristic, complemented
5#14521372C211yesmaximal, characteristic, complemented
6#14521351C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521275C211yesmaximal, characteristic, complemented
9#14521269C211yesmaximal, characteristic, complemented
10#14521208C211yesmaximal, characteristic, complemented
11SD16×Dic31C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
13#14521042C211yesmaximal, characteristic, complemented
14C2×#11758420C211yesmaximal, characteristic, complemented
15C31×#450C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C2×#92497C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic
20C31×C22⋊Q8C2211yescharacteristic
21#11758530—21no—
22C2×C22⋊Dic31—21no—
23#11758523C2211yescharacteristic, complemented
24Q8×Dic31C2211yescharacteristic, complemented
25C2×#92482C2211yescharacteristic, complemented
26#11758516—21no—
27#11758515C2211yescharacteristic
28#11758513C2211yescharacteristic
29#11758512—21no—
30D4×Dic31C2211yescharacteristic
31C4×C22⋊D31C2211yescharacteristic
32C2×C4⋊Dic31C2211yescharacteristic
33#11758501C2211yescharacteristic
34C22×C31⋊C8C2211yescharacteristic
35C2×C8×D31C2211yescharacteristic, complemented
36#11758475—21no—
37#11758469C2211yescharacteristic, complemented
38#11758467—21no—
39#11758467C2211yescharacteristic, complemented
40#11758463—21no—
41#11758454—21no—
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic
45#11758423C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic, complemented
51#11758405C2211yescharacteristic, complemented
52#11758405C2211yescharacteristic, complemented
53#11758404C2211yescharacteristic, complemented
54#11758404C2211yescharacteristic, complemented
55Dic31⋊C8C2211yescharacteristic, complemented
56C8×Dic31C2211yescharacteristic, complemented
57#11758398C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C24×C31—21no—
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31—22no—
62C2×D4×C31—21no—
63C2×D4×C31—41no—
64C2×D4×C31C2311yescharacteristic
65C2×D4×C31C2311yescharacteristic
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31D411yescharacteristic
70C22×Dic31—21no—
71C22×Dic31—21no—
72C22×Dic31—21no—
73#92497—22no—
74#92497—41no—
75C2×C4×D31C2311yescharacteristic
76C2×Dic62C2311yescharacteristic
77SD16×C31—22no—
78SD16×C31—41no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89C22⋊Dic31D411yescharacteristic
90#92482—41no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4D411yescharacteristic
94C4⋊Dic31—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C8×D31—41no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31—42no—
114C23×C31—42no—
115C23×C31—81no—
116C23×C31C2×D411yescharacteristic
117C22×D31C2×D411yescharacteristic
118Q8×C31—21no—
119Q8×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122D4×C31—21no—
123D4×C31—42no—
124D4×C31#4112yes—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2411yescharacteristic
131C22⋊D31—22no—
132C22⋊D31—42no—
133C22⋊D31—81no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138C2×Dic31—42no—
139C2×Dic31—42no—
140C2×Dic31—81no—
141C2×Dic31C2×D411yescharacteristic
142C2×Dic31C2×D411yescharacteristic
143C2×Dic31C2×D411yescharacteristic
144C4×D31—21no—
145C4×D31—21no—
146Dic62—21no—
147Dic62—21no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3296—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—22no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—84no—
162C22×C31#13512yes—
163C22×C31C22×D411yescharacteristic
164C2×D31—21no—
165C2×D31—21no—
166C2×D31—21no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—21no—
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178Dic31—41no—
179#552—311no—
180#546—311no—
181#488—311no—
182#483—311no—
183#482—311no—
184#478—311no—
185#467—311no—
186#465—311no—
187#464—311no—
188#452—311no—
189#450D3111yescharacteristic, complemented
190C4×SD16—311no—
191C8×D4—311no—
192#416—311no—
193C2×#102—311no—
194C2×C31—22no—
195C2×C31—42no—
196C2×C31—81no—
197C2×C31#54611yescharacteristic
198C2×C31C2×#13511yescharacteristic
199C2×C31#57711yescharacteristic
200D31—41no—
201C2×#41—311no—
202C22×D4C2×D3111yescharacteristic
203C2×Q16—311no—
204C2×SD16C2×D3111yescharacteristic
205C2×SD16C2×D3111yescharacteristic
206C22×C8—311no—
207C22×C8—311no—
208#126—621no—
209#125—311no—
210#125—621no—
211#124—311no—
212#123—621no—
213#123—621no—
214C22⋊Q8—311no—
215C22⋊Q8—311no—
216C22⋊Q8C2×D3111yescharacteristic
217#121—311no—
218#121—621no—
219#120—621no—
220C4×Q8—311no—
221C4×D4—311no—
222C4×D4—311no—
223#117—311no—
224#117—621no—
225C2×C4⋊C4—311no—
226C2×C22⋊C4—621no—
227#107—311no—
228#106—311no—
229#106—311no—
230C4⋊C8—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103—311no—
235#102—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102C2×D3111yescharacteristic
240#102C2×D3111yescharacteristic
241C22⋊C8—311no—
242C22⋊C8C2×D3111yescharacteristic
243C4×C8—311no—
244C31#329611yescharacteristic, complemented, Sylow
245C24—21no—
246#41—622no—
247#41—1241no—
248C2×Q8—311no—
249C2×Q8C22×D3111yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—311no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4C22×D3111yescharacteristic
257C2×D4C22×D3111yescharacteristic
258C22×C4—311no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4C22×D3111yescharacteristic
263Q16—1241no—
264SD16—22no—
265SD16—41no—
266C2×C8—311no—
267C2×C8—311no—
268C2×C8—1241no—
269C2×C8—1241no—
270C2×C8C22×D3111yescharacteristic
271C2×C8C22×D3111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—311no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4—621no—
283C4⋊C4C22×D3111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—311no—
286C22⋊C4—311no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C42—311no—
295C42—621no—
296C42—621no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—311no—
303C23D4×D3111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—621no—
307Q8—621no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—622no—
313D4—1242no—
314D4—2481no—
315D4#9249712yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—1242no—
330C2×C4—1242no—
331C2×C4—2481no—
332C2×C4D4×D3111yescharacteristic
333C2×C4C23×D3111yescharacteristic
334C8—21no—
335C8—21no—
336C8—621no—
337C8—621no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—621no—
348C22—621no—
349C22—621no—
350C22#1175849312yes—
351C22C2×D4×D3111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—621no—
356C4—621no—
357C4—621no—
358C4—1241no—
359C4—1241no—
360C4—1241no—
361C4—1241no—
362C4C2×#9249711yescharacteristic
363C4#1175856111yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—1241no—
368C2#1452168611yescharacteristic
369C2C2×#1175849311yescharacteristic
370C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#450C2
socleC22×C31C22×D4
prime radical#14521693C2
hypercenter#450D31
hypocenterC31#3296
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14521741C2semidirect
3. #14521402C2semidirect
4. #14521380C2semidirect
5. #14521372C2semidirect
6. #14521351C2semidirect
7. #14521288C2semidirect
8. #14521275C2semidirect
9. #14521269C2semidirect
10. #14521208C2semidirect
11. SD16×Dic31C2semidirect
12. (C22⋊D31)⋊C8C2semidirect
13. #14521042C2semidirect
14. C2×#11758420C2semidirect
15. C31×#450C2semidirect
23. #11758523C22semidirect
24. Q8×Dic31C22semidirect
25. C2×#92482C22semidirect
35. C2×C8×D31C22semidirect
37. #11758469C22semidirect
39. #11758467C22semidirect
45. #11758423C22semidirect
50. (C2×D31)⋊C8C22semidirect
51. #11758405C22semidirect
52. #11758405C22semidirect
53. #11758404C22semidirect
54. #11758404C22semidirect
55. Dic31⋊C8C22semidirect
56. C8×Dic31C22semidirect
57. #11758398C22semidirect
58. #11758395C22semidirect
189. #450D31semidirect
244. C31#3296semidirect

Maximal subgroups

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

subgroupindex
#145217412
#145216932
#145214022
#145213802
#145213722
#145213512
#145212882
#145212752
#145212692
#145212082
SD16×Dic312
(C22⋊D31)⋊C82
#145210422
C2×#117584202
C31×#4502
#329631