Finite Group Databasebeta

← #16855897

Subgroups — #16855897

Order 3968.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521670C211yesmaximal, characteristic, complemented
2#14521523C211yesmaximal, characteristic, complemented
3#14521391C211yesmaximal, characteristic, complemented
4#14521374C211yesmaximal, characteristic, complemented
5#14521340C211yesmaximal, characteristic, complemented
6#14521330C211yesmaximal, characteristic, complemented
7#14521265C211yesmaximal, characteristic, complemented
8#14521265C211yesmaximal, characteristic, complemented
9#14521202C211yesmaximal, characteristic, complemented
10#14521185C211yesmaximal, characteristic
11#14521162C211yesmaximal, characteristic, complemented
12#14521151C211yesmaximal, characteristic, complemented
13C4×#92470C211yesmaximal, characteristic, complemented
14C4×D248C211yesmaximal, characteristic, complemented
15C31×#433C211yesmaximal, characteristic, complemented
16C22×D124C2211yescharacteristic
17C31×#117C2211yescharacteristic
18#11758507C2211yescharacteristic
19#11758503C2211yescharacteristic
20#11758501C2211yescharacteristic
21C2×D248C2211yescharacteristic
22C2×D248C2211yescharacteristic
23C2×#92470C2211yescharacteristic
24C2×#92470C2211yescharacteristic
25#11758475—21no—
26#11758473—21no—
27#11758470—21no—
28#11758470—21no—
29#11758462—21no—
30#11758460—21no—
31C22⋊C4×D31—21no—
32C22⋊C4×D31—21no—
33#11758452C2211yescharacteristic, complemented
34C4×D124C2211yescharacteristic
35C4×D124C2211yescharacteristic
36C4×D124C2211yescharacteristic
37C4×D124C2211yescharacteristic
38C4×D124C2211yescharacteristic, complemented
39#11758446C2211yescharacteristic, complemented
40C4×Dic62C2211yescharacteristic, complemented
41C31×C4⋊C8C2211yescharacteristic, complemented
42C31×C4⋊C8C2211yescharacteristic, complemented
43C31×C22⋊C8C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic
45C31×#97C2211yescharacteristic, complemented
46C4×C8×C31C2211yescharacteristic, complemented
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic, complemented
52#11758409C2211yescharacteristic, complemented
53#11758406C2211yescharacteristic, complemented
54#11758406C2211yescharacteristic, complemented
55#11758405C2211yescharacteristic, complemented
56#11758405C2211yescharacteristic, complemented
57#11758404C2211yescharacteristic, complemented
58#11758404C2211yescharacteristic, complemented
59C23×D31—21no—
60C22×C4×C31C2311yescharacteristic
61C2×C22⋊D31—21no—
62C2×D124—21no—
63C2×D124—22no—
64C2×D124—22no—
65C2×D124C2311yescharacteristic
66C2×D124C2311yescharacteristic
67C2×D124C2311yescharacteristic
68C2×C4×D31—21no—
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×Dic62—21no—
74C2×Dic62C2311yescharacteristic
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C2×C8×C31C2311yescharacteristic
79C4⋊C4×C31D411yescharacteristic
80C4⋊C4×C31D411yescharacteristic
81C22⋊C4×C31D411yescharacteristic
82C22⋊C4×C31D411yescharacteristic
83C42×C31C2311yescharacteristic
84C42×C31C2311yescharacteristic
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95C4⋊Dic31—21no—
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104D248—22no—
105D248—22no—
106#92470—22no—
107#92470—22no—
108C23×C31C2×D411yescharacteristic
109C22×D31—21no—
110C22×D31—21no—
111C22×D31—24no—
112C22×D31—21no—
113C22×D31—81no—
114C22×D31—81no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31C2×D411yescharacteristic
118C2×C4×C31C2×D411yescharacteristic
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31C2×D411yescharacteristic
121C2×C4×C31C2×D411yescharacteristic
122C2×C4×C31C2411yescharacteristic
123C22⋊D31—81no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129D124—24no—
130D124—21no—
131D124—21no—
132D124—21no—
133D124—21no—
134D124#4112yes—
135D124#4112yes—
136C4×D31—81no—
137C4×D31—81no—
138C4×D31—81no—
139C4×D31—81no—
140C4×D31—81no—
141Dic62—21no—
142Dic62—21no—
143Dic62—81no—
144C8×C31—21no—
145C8×C31—21no—
146C8×C31—21no—
147C8×C31—21no—
148#3118—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—21no—
152C22×C31C22×D411yescharacteristic
153C2×D31—22no—
154C2×D31—22no—
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—84no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31C2×#4111yescharacteristic
169C4×C31C2×#4111yescharacteristic
170Dic31—41no—
171Dic31—41no—
172Dic31—41no—
173Dic31—41no—
174Dic31—41no—
175#542—311no—
176#518—311no—
177#485—311no—
178#482—311no—
179#476—311no—
180#474—311no—
181#463—311no—
182#463—311no—
183#450—311no—
184#447—311no—
185#442—311no—
186#440—311no—
187C4×SD16—311no—
188C4×D8—311no—
189#433D3111yescharacteristic, complemented
190C2×C31—41no—
191C2×C31#52511yescharacteristic
192C2×C31#57611yescharacteristic
193C2×C31#57711yescharacteristic
194D31—42no—
195D31—42no—
196D31—81no—
197C22×D4—311no—
198C2×SD16—311no—
199C2×SD16—311no—
200C2×D8—311no—
201C2×D8—311no—
202C4⋊Q8—311no—
203#126—621no—
204#124—311no—
205#124—621no—
206#123—621no—
207C22⋊Q8—311no—
208C22⋊Q8—621no—
209#121—311no—
210C4×Q8—311no—
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—621no—
217C4×D4—621no—
218#117—311no—
219#117C2×D3111yescharacteristic
220C2×C22⋊C4—621no—
221C2×C22⋊C4—621no—
222#107—311no—
223#107—311no—
224#106—311no—
225#106—311no—
226C4⋊C8C2×D3111yescharacteristic, complemented
227C4⋊C8C2×D3111yescharacteristic, complemented
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102—311no—
235#102—311no—
236C22⋊C8C2×D3111yescharacteristic
237C22⋊C8C2×D3111yescharacteristic
238#97C2×D3111yescharacteristic, complemented
239C4×C8C2×D3111yescharacteristic, complemented
240C31#311811yescharacteristic, complemented, Sylow
241C24—621no—
242C2×Q8—311no—
243C2×Q8—621no—
244C2×D4—311no—
245C2×D4—311no—
246C2×D4—311no—
247C2×D4—622no—
248C2×D4—622no—
249C2×D4—621no—
250C2×D4—621no—
251C22×C4—621no—
252C22×C4—621no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4C22×D3111yescharacteristic
257SD16—622no—
258SD16—622no—
259D8—622no—
260D8—622no—
261C2×C8C22×D3111yescharacteristic
262C2×C8C22×D3111yescharacteristic
263C2×C8C22×D3111yescharacteristic
264C2×C8C22×D3111yescharacteristic
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4D12411yescharacteristic
273C4⋊C4D12411yescharacteristic
274C22⋊C4—621no—
275C22⋊C4—621no—
276C22⋊C4—621no—
277C22⋊C4—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4D12411yescharacteristic
285C22⋊C4D12411yescharacteristic
286C42—621no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C42C22×D3111yescharacteristic
290C23—624no—
291C23—621no—
292C23—621no—
293C23—621no—
294C23—2481no—
295C23—2481no—
296C23C2×D12411yescharacteristic
297Q8—621no—
298Q8—621no—
299Q8—2481no—
300D4—312no—
301D4—312no—
302D4—624no—
303D4—621no—
304D4—621no—
305D4—621no—
306D4—621no—
307D4—2481no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—2481no—
316C2×C4—2481no—
317C2×C4—2481no—
318C2×C4—2481no—
319C2×C4—2481no—
320C2×C4C2×D12411yescharacteristic
321C2×C4C2×D12411yescharacteristic
322C2×C4C2×D12411yescharacteristic
323C2×C4C2×D12411yescharacteristic
324C2×C4C2×D12411yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—622no—
334C22—622no—
335C22—1241no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22—1241no—
342C22—2484no—
343C22C22×D12411yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—1241no—
350C4—1241no—
351C4—1241no—
352C4—1241no—
353C4—1241no—
354C4#41×D3111yescharacteristic
355C4#41×D3111yescharacteristic
356C2—41no—
357C2—1242no—
358C2—1242no—
359C2—2481no—
360C2#1452156111yescharacteristic
361C2#1452185411yescharacteristic
362C2#1452186111yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#433C2
socleC22×C31C22×D4
prime radical#14521185C2
hypercenter#433D31
hypocenterC31#3118
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14521670C2semidirect
2. #14521523C2semidirect
3. #14521391C2semidirect
4. #14521374C2semidirect
5. #14521340C2semidirect
6. #14521330C2semidirect
7. #14521265C2semidirect
8. #14521265C2semidirect
9. #14521202C2semidirect
11. #14521162C2semidirect
12. #14521151C2semidirect
13. C4×#92470C2semidirect
14. C4×D248C2semidirect
15. C31×#433C2semidirect
33. #11758452C22semidirect
38. C4×D124C22semidirect
39. #11758446C22semidirect
40. C4×Dic62C22semidirect
41. C31×C4⋊C8C22semidirect
42. C31×C4⋊C8C22semidirect
45. C31×#97C22semidirect
46. C4×C8×C31C22semidirect
51. #11758409C22semidirect
52. #11758409C22semidirect
53. #11758406C22semidirect
54. #11758406C22semidirect
55. #11758405C22semidirect
56. #11758405C22semidirect
57. #11758404C22semidirect
58. #11758404C22semidirect
189. #433D31semidirect
226. C4⋊C8C2×D31semidirect
227. C4⋊C8C2×D31semidirect
238. #97C2×D31semidirect
239. C4×C8C2×D31semidirect
240. C31#3118semidirect

Maximal subgroups

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

subgroupindex
#145216702
#145215232
#145213912
#145213742
#145213402
#145213302
#145212652
#145212022
#145211852
#145211622
#145211512
C4×#924702
C4×D2482
C31×#4332
#311831