Finite Group Databasebeta

← #16857551

Subgroups — #16857551

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#14521740C211yesmaximal, characteristic, complemented
2#14521694C211yesmaximal, characteristic
3#14521404C211yesmaximal, characteristic, complemented
4#14521381C211yesmaximal, characteristic, complemented
5#14521375C211yesmaximal, characteristic, complemented
6#14521349C211yesmaximal, characteristic, complemented
7#14521289C211yesmaximal, characteristic, complemented
8#14521281C211yesmaximal, characteristic, complemented
9#14521271C211yesmaximal, characteristic, complemented
10#14521208C211yesmaximal, characteristic, complemented
11#14521198C211yesmaximal, characteristic, complemented
12C8×D124C211yesmaximal, characteristic, complemented
13#14521042C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C4×SD16×C31C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×D4×D31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic, complemented
20C4×D4×C31C2211yescharacteristic
21#11758523C2211yescharacteristic
22#11758523C2211yescharacteristic, complemented
23C2×#92482C2211yescharacteristic, complemented
24C2×#92481C2211yescharacteristic
25#11758507—21no—
26C2×(C2×D31)⋊C4—21no—
27C2×C8×D31C2211yescharacteristic
28C2×C8×D31C2211yescharacteristic, complemented
29#11758474C2211yescharacteristic
30#11758472C2211yescharacteristic
31#11758471—21no—
32#11758469C2211yescharacteristic, complemented
33C4⋊C4×D31C2211yescharacteristic
34#11758466—21no—
35#11758463—21no—
36#11758459—21no—
37#11758453—21no—
38#11758452C2211yescharacteristic
39C4×D124C2211yescharacteristic
40#11758449—21no—
41#11758447C2211yescharacteristic, complemented
42C31×#106C2211yescharacteristic, complemented
43C31×#103C2211yescharacteristic, complemented
44C31×#102C2211yescharacteristic
45C4×C8×C31C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic, complemented
52#11758404C2211yescharacteristic, complemented
53#11758404C2211yescharacteristic, complemented
54#11758398C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758396C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58C4⋊(C31⋊C8)C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C22×Dic31—21no—
66#92497—22no—
67#92497—41no—
68D4×D31—22no—
69D4×D31—41no—
70C2×D124—21no—
71C2×D124D411yescharacteristic
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31C2311yescharacteristic
75C2×C4×D31C2311yescharacteristic
76C2×Dic62C2311yescharacteristic
77SD16×C31—22no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31—21no—
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C42×C31—21no—
85C42×C31C2311yescharacteristic
86#92482—41no—
87#92481—41no—
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—
95(C2×D31)⋊C4D411yescharacteristic
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31D411yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106C4×Dic31—21no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C8×D31—41no—
110C8×D31—41no—
111C23×C31—21no—
112C22×D31—21no—
113C22×D31—42no—
114C22×D31—42no—
115C22×D31—81no—
116C22×D31C2×D411yescharacteristic
117C22×D31C2×D411yescharacteristic
118Q8×C31—21no—
119Q8×C31—21no—
120D4×C31—21no—
121D4×C31#4112yes—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—81no—
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2411yescharacteristic
129C22⋊D31—42no—
130C22⋊D31—42no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—42no—
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137D124—22no—
138D124—21no—
139D124—21no—
140D124—81no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—21no—
144C4×D31—21no—
145C4×D31—42no—
146Dic62—21no—
147Dic62—21no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3296—311nomaximal, Sylow
153C22×C31—22no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—84no—
166C2×D31#13512yes—
167C4×C31—21no—
168C4×C31—21no—
169C4×C31—41no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31C2×#4111yescharacteristic
173C4×C31H(5,𝔽2)11yescharacteristic
174Dic31—21no—
175Dic31—21no—
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#450—311no—
190C4×SD16D3111yescharacteristic, complemented
191C8×D4—311no—
192#416—311no—
193C2×#102—311no—
194C2×C31—42no—
195C2×C31#54611yescharacteristic
196C2×C31C2×#13511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—22no—
199D31—41no—
200D31—81no—
201C2×#41—311no—
202C22×D4—311no—
203C2×Q16—311no—
204C2×SD16—311no—
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⋊Q8—311no—
217#121—311no—
218#121—621no—
219#120—621no—
220C4×Q8C2×D3111yescharacteristic, complemented
221C4×D4—311no—
222C4×D4C2×D3111yescharacteristic
223#117—311no—
224#117—621no—
225C2×C4⋊C4—311no—
226C2×C22⋊C4—621no—
227#107—311no—
228#106—311no—
229#106C2×D3111yescharacteristic, complemented
230C4⋊C8—311no—
231#103—311no—
232#103—311no—
233#103—311no—
234#103C2×D3111yescharacteristic, complemented
235#102—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102C2×D3111yescharacteristic
241C22⋊C8—311no—
242C22⋊C8—311no—
243C4×C8C2×D3111yescharacteristic, complemented
244C31#329611yescharacteristic, complemented, Sylow
245C24—621no—
246#41—622no—
247#41—1241no—
248C2×Q8—311no—
249C2×Q8C22×D3111yescharacteristic
250C2×D4—311no—
251C2×D4—311no—
252C2×D4—621no—
253C2×D4—621no—
254C2×D4—622no—
255C2×D4—621no—
256C2×D4—1241no—
257C2×D4C22×D3111yescharacteristic
258C22×C4—21no—
259C22×C4—311no—
260C22×C4—311no—
261C22×C4—621no—
262C22×C4—621no—
263Q16—1241no—
264SD16—22no—
265SD16—1241no—
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—621no—
277C4⋊C4—621no—
278C4⋊C4—621no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4C22×D3111yescharacteristic
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—21no—
295C42—621no—
296C42C22×D3111yescharacteristic
297C23—21no—
298C23—311no—
299C23—311no—
300C23—621no—
301C23—1242no—
302C23—1242no—
303C23—2481no—
304Q8—21no—
305Q8—21no—
306Q8—621no—
307Q8—621no—
308D4—21no—
309D4—622no—
310D4—621no—
311D4—621no—
312D4—1242no—
313D4—1242no—
314D4—2481no—
315D4#9249512yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—621no—
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×C4D4×D3111yescharacteristic
332C2×C4D4×D3111yescharacteristic
333C2×C4C23×D3111yescharacteristic
334C8—21no—
335C8—21no—
336C8—621no—
337C8—621no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—312no—
342C22—621no—
343C22—621no—
344C22—621no—
345C22—621no—
346C22—621no—
347C22—1241no—
348C22—1241no—
349C22—1241no—
350C22—2484no—
351C22C2×D4×D3111yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—621no—
358C4—621no—
359C4—1241no—
360C4—1241no—
361C4—1241no—
362C4C2×#9249511yescharacteristic
363C4#1175856611yescharacteristic
364C2—42no—
365C2—622no—
366C2—1241no—
367C2—2481no—
368C2#1452169511yescharacteristic
369C2#135×D3111yescharacteristic
370C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×SD16×C31C2
socleC22×C31C22×D4
prime radical#14521694C2
hypercenterC4×SD16D31
hypocenterC31#3296
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14521740C2semidirect
3. #14521404C2semidirect
4. #14521381C2semidirect
5. #14521375C2semidirect
6. #14521349C2semidirect
7. #14521289C2semidirect
8. #14521281C2semidirect
9. #14521271C2semidirect
10. #14521208C2semidirect
11. #14521198C2semidirect
12. C8×D124C2semidirect
13. #14521042C2semidirect
14. #102×D31C2semidirect
15. C4×SD16×C31C2semidirect
19. C4×Q8×C31C22semidirect
22. #11758523C22semidirect
23. C2×#92482C22semidirect
28. C2×C8×D31C22semidirect
32. #11758469C22semidirect
41. #11758447C22semidirect
42. C31×#106C22semidirect
43. C31×#103C22semidirect
45. C4×C8×C31C22semidirect
51. (C2×D31)⋊C8C22semidirect
52. #11758404C22semidirect
53. #11758404C22semidirect
54. #11758398C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. C4⋊(C31⋊C8)C22semidirect
190. C4×SD16D31semidirect
220. C4×Q8C2×D31semidirect
229. #106C2×D31semidirect
234. #103C2×D31semidirect
243. C4×C8C2×D31semidirect
244. C31#3296semidirect

Maximal subgroups

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

subgroupindex
#145217402
#145216942
#145214042
#145213812
#145213752
#145213492
#145212892
#145212812
#145212712
#145212082
#145211982
C8×D1242
#145210422
#102×D312
C4×SD16×C312
#329631