Finite Group Databasebeta

← #16857668

Subgroups — #16857668

Order 3968.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521700C211yesmaximal, characteristic, complemented
2#14521693C211yesmaximal, characteristic, complemented
3#14521407C211yesmaximal, characteristic, complemented
4#14521379C211yesmaximal, characteristic, complemented
5#14521366C211yesmaximal, characteristic, complemented
6#14521337C211yesmaximal, characteristic, complemented
7#14521301C211yesmaximal, characteristic, complemented
8#14521278C211yesmaximal, characteristic, complemented
9#14521263C211yesmaximal, characteristic, complemented
10#14521195C211yesmaximal, characteristic, complemented
11#14521183C211yesmaximal, characteristic, complemented
12#14521158C211yesmaximal, characteristic, complemented
13#14521120C211yesmaximal, characteristic, complemented
14#14521047C211yesmaximal, characteristic, complemented
15C2×C31×#102C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C2×#92497C2211yescharacteristic
18C2×#92495—21no—
19C22×C8×C31C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21#11758530—21no—
22C2×C22⋊Dic31—21no—
23#11758516—21no—
24#11758515C2211yescharacteristic
25#11758513C2211yescharacteristic
26#11758512—21no—
27D4×Dic31C2211yescharacteristic
28C2×#92479C2211yescharacteristic
29C2×#92479C2211yescharacteristic
30#11758507C2211yescharacteristic
31#11758506—21no—
32C4×C22⋊D31C2211yescharacteristic
33#11758501C2211yescharacteristic
34C2×#92470C2211yescharacteristic, complemented
35C2×#92469C2211yescharacteristic, complemented
36#11758473—21no—
37#11758472C2211yescharacteristic, complemented
38#11758471—21no—
39#11758470C2211yescharacteristic, complemented
40C4⋊C4×D31C2211yescharacteristic, complemented
41#11758465C2211yescharacteristic, complemented
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758409C2211yescharacteristic, complemented
50(C2×D31)⋊C8C2211yescharacteristic, complemented
51#11758405C2211yescharacteristic, complemented
52#11758404C2211yescharacteristic, complemented
53#11758403C2211yescharacteristic, complemented
54Dic31⋊C8C2211yescharacteristic, complemented
55#11758398C2211yescharacteristic, complemented
56#11758398C2211yescharacteristic, complemented
57#11758396C2211yescharacteristic, complemented
58#11758396C2211yescharacteristic, complemented
59C24×C31—21no—
60C2×D4×C31—22no—
61C2×D4×C31—21no—
62C2×D4×C31—41no—
63C2×D4×C31C2311yescharacteristic
64C2×D4×C31C2311yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31D411yescharacteristic
71C22×Dic31—21no—
72C22×Dic31—21no—
73#92497—22no—
74#92497—41no—
75#92495—44no—
76C2×D124—21no—
77C2×D124C2311yescharacteristic
78C2×C4×D31—21no—
79C2×C4×D31—21no—
80C2×C4×D31C2311yescharacteristic
81C2×Dic62—21no—
82C2×Dic62C2311yescharacteristic
83C2×C8×C31—41no—
84C2×C8×C31C2311yescharacteristic
85C2×C8×C31C2311yescharacteristic
86C4⋊C4×C31—21no—
87C4⋊C4×C31C2311yescharacteristic
88C4⋊C4×C31C2311yescharacteristic
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92C22⋊Dic31—21no—
93C22⋊Dic31—21no—
94C22⋊Dic31D411yescharacteristic
95#92479—22no—
96#92479—41no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4—21no—
99(C2×D31)⋊C4—21no—
100(C2×D31)⋊C4D411yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106Dic31⋊C4D411yescharacteristic
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110#92470—41no—
111#92469—41no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—42no—
115C23×C31—42no—
116C23×C31—81no—
117C23×C31C2×D411yescharacteristic
118C22×D31—21no—
119C22×D31C2×D411yescharacteristic
120D4×C31—21no—
121D4×C31—21no—
122D4×C31—21no—
123D4×C31—42no—
124D4×C31#4112yescomplemented
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—42no—
130C2×C4×C31C2×D411yescharacteristic
131C2×C4×C31C2411yescharacteristic
132C22⋊D31—22no—
133C22⋊D31—42no—
134C22⋊D31—42no—
135C22⋊D31—81no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138C2×Dic31—21no—
139C2×Dic31—42no—
140C2×Dic31—81no—
141C2×Dic31C2×D411yescharacteristic
142C2×Dic31C2×D411yescharacteristic
143C2×Dic31C2×D411yescharacteristic
144D124—21no—
145D124—21no—
146D124—42no—
147C4×D31—21no—
148C4×D31—21no—
149C4×D31—42no—
150C4×D31—42no—
151Dic62—21no—
152Dic62—21no—
153Dic62—42no—
154C8×C31—21no—
155C8×C31—21no—
156C31⋊C8—21no—
157C31⋊C8—21no—
158#3306—311nomaximal, Sylow
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—22no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—84no—
168C22×C31AGL(1,ℤ/8)12yes—
169C22×C31C22×D411yescharacteristic
170C2×D31—21no—
171C2×D31—21no—
172C2×D31—21no—
173C2×D31—41no—
174C2×D31—41no—
175C2×D31—41no—
176C4×C31—21no—
177C4×C31—41no—
178C4×C31—41no—
179C4×C31C2×#4111yescharacteristic
180C4×C31H(5,𝔽2)11yescharacteristic
181Dic31—21no—
182Dic31—21no—
183Dic31—21no—
184Dic31—41no—
185Dic31—41no—
186Dic31—41no—
187#547—311no—
188#546—311no—
189#489—311no—
190#483—311no—
191#481—311no—
192#476—311no—
193#469—311no—
194#465—311no—
195#463—311no—
196#449—311no—
197#447—311no—
198#442—311no—
199#435—311no—
200#417—311no—
201C2×#102D3111yescharacteristic, complemented
202C2×C31—22no—
203C2×C31—42no—
204C2×C31—81no—
205C2×C31#54611yescharacteristic
206C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C31#57711yescharacteristic
208D31—41no—
209D31—81no—
210C2×#41—311no—
211C2×#41—621no—
212C22×D4C2×D3111yescharacteristic
213C2×SD16—311no—
214C2×D8—311no—
215C2×D8—311no—
216C2×M16—311no—
217C22×C8C2×D3111yescharacteristic
218C4⋊Q8—311no—
219#124—311no—
220#123—621no—
221#123—621no—
222#123—621no—
223C22⋊Q8—311no—
224C22⋊Q8—621no—
225#121—311no—
226#121—311no—
227#121—311no—
228#121—621no—
229#120—621no—
230C4×D4—311no—
231C4×D4—311no—
232C4×D4—311no—
233C2×C4⋊C4—311no—
234C2×C4⋊C4C2×D3111yescharacteristic
235C2×C22⋊C4—621no—
236#106—311no—
237#106—311no—
238#106—311no—
239C4⋊C8—311no—
240#103—311no—
241#103—311no—
242#103—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246#102C2×D3111yescharacteristic
247#102C2×D3111yescharacteristic
248#102C2×D3111yescharacteristic
249#102C2×D3111yescharacteristic
250C22⋊C8—311no—
251C22⋊C8—311no—
252#97—311no—
253C31#330611yescharacteristic, complemented, Sylow
254C24—21no—
255#41—622no—
256#41—1244no—
257#41—1241no—
258C2×Q8—311no—
259C2×Q8—621no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—311no—
264C2×D4—311no—
265C2×D4—621no—
266C2×D4—621no—
267C2×D4—621no—
268C2×D4—621no—
269C2×D4C22×D3111yescharacteristic
270C2×D4C22×D3111yescharacteristic
271C22×C4—21no—
272C22×C4—311no—
273C22×C4—621no—
274C22×C4—621no—
275C22×C4—621no—
276C22×C4—621no—
277C22×C4C22×D3111yescharacteristic
278SD16—1241no—
279D8—622no—
280D8—1241no—
281M16—1241no—
282C2×C8—41no—
283C2×C8—311no—
284C2×C8—311no—
285C2×C8C22×D3111yescharacteristic
286C2×C8C22×D3111yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—311no—
289C4⋊C4—311no—
290C4⋊C4—311no—
291C4⋊C4—621no—
292C4⋊C4—621no—
293C4⋊C4—621no—
294C4⋊C4C22×D3111yescharacteristic
295C4⋊C4C22×D3111yescharacteristic
296C22⋊C4—311no—
297C22⋊C4—311no—
298C22⋊C4—621no—
299C22⋊C4—621no—
300C22⋊C4—621no—
301C22⋊C4—621no—
302C22⋊C4—621no—
303C22⋊C4—621no—
304C22⋊C4—621no—
305C22⋊C4—621no—
306C42—311no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—311no—
313C23—621no—
314C23D4×D3111yescharacteristic
315Q8—621no—
316Q8—621no—
317Q8—1242no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—622no—
323D4—621no—
324D4—621no—
325D4—1242no—
326D4—1242no—
327D4—1242no—
328D4—2481no—
329D4#9249512yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—311no—
336C2×C4—311no—
337C2×C4—311no—
338C2×C4—621no—
339C2×C4—621no—
340C2×C4—621no—
341C2×C4—621no—
342C2×C4—621no—
343C2×C4—1242no—
344C2×C4—1242no—
345C2×C4—1242no—
346C2×C4—2481no—
347C2×C4D4×D3111yescharacteristic
348C2×C4C23×D3111yescharacteristic
349C8—21no—
350C8—21no—
351C8—621no—
352C8—621no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22—621no—
363C22—621no—
364C22—621no—
365C22—1241no—
366C22—1241no—
367C22—1241no—
368C22#1175848812yes—
369C22C2×D4×D3111yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—621no—
374C4—621no—
375C4—621no—
376C4—1241no—
377C4—1241no—
378C4—1241no—
379C4C2×#9249511yescharacteristic
380C4#1175856111yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—1241no—
385C2—2481no—
386C2#1452168911yescharacteristic
387C2C2×#1175848811yescharacteristic
388C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#102C2
socleC22×C31C22×D4
hypercenterC2×#102D31
hypocenterC31#3306
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14521700C2semidirect
2. #14521693C2semidirect
3. #14521407C2semidirect
4. #14521379C2semidirect
5. #14521366C2semidirect
6. #14521337C2semidirect
7. #14521301C2semidirect
8. #14521278C2semidirect
9. #14521263C2semidirect
10. #14521195C2semidirect
11. #14521183C2semidirect
12. #14521158C2semidirect
13. #14521120C2semidirect
14. #14521047C2semidirect
15. C2×C31×#102C2semidirect
34. C2×#92470C22semidirect
35. C2×#92469C22semidirect
37. #11758472C22semidirect
39. #11758470C22semidirect
40. C4⋊C4×D31C22semidirect
41. #11758465C22semidirect
49. #11758409C22semidirect
50. (C2×D31)⋊C8C22semidirect
51. #11758405C22semidirect
52. #11758404C22semidirect
53. #11758403C22semidirect
54. Dic31⋊C8C22semidirect
55. #11758398C22semidirect
56. #11758398C22semidirect
57. #11758396C22semidirect
58. #11758396C22semidirect
124. D4×C31#41semidirect
201. C2×#102D31semidirect
253. C31#3306semidirect
329. D4#92495semidirect

Maximal subgroups

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

subgroupindex
#145217002
#145216932
#145214072
#145213792
#145213662
#145213372
#145213012
#145212782
#145212632
#145211952
#145211832
#145211582
#145211202
#145210472
C2×C31×#1022
#330631