Finite Group Databasebeta

← #16857552

Subgroups — #16857552

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#14521690C211yesmaximal, characteristic
3#14521405C211yesmaximal, characteristic, complemented
4#14521377C211yesmaximal, characteristic, complemented
5#14521376C211yesmaximal, characteristic, complemented
6#14521352C211yesmaximal, characteristic, complemented
7#14521281C211yesmaximal, characteristic, complemented
8#14521273C211yesmaximal, characteristic, complemented
9#14521210C211yesmaximal, characteristic, complemented
10#14521199C211yesmaximal, characteristic, complemented
11#14521134C211yesmaximal, characteristic, complemented
12C8×C22⋊D31C211yesmaximal, characteristic, complemented
13#14521044C211yesmaximal, characteristic, complemented
14C2×#11758409C211yesmaximal, characteristic, complemented
15C31×#467C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C22×D124C2211yescharacteristic
18C2×Q16×C31C2211yescharacteristic, complemented
19C22×C8×C31C2211yescharacteristic
20C31×C22⋊Q8C2211yescharacteristic
21C31×C22⋊Q8C2211yescharacteristic
22#11758524C2211yescharacteristic
23#11758523C2211yescharacteristic, complemented
24Q8×Dic31C2211yescharacteristic, complemented
25C2×#92481C2211yescharacteristic
26C2×#92481C2211yescharacteristic
27C4×C22⋊D31C2211yescharacteristic
28C2×C4⋊Dic31C2211yescharacteristic
29C2×C8×D31C2211yescharacteristic, complemented
30#11758475—21no—
31#11758472—21no—
32#11758472C2211yescharacteristic
33#11758471—21no—
34#11758470C2211yescharacteristic
35#11758469C2211yescharacteristic, complemented
36#11758467—21no—
37#11758467C2211yescharacteristic, complemented
38#11758463—21no—
39#11758459—21no—
40C22⋊C4×D31—21no—
41#11758454—21no—
42C31×#107C2211yescharacteristic, complemented
43C31×#103C2211yescharacteristic, complemented
44C31×#103C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758423C2211yescharacteristic, complemented
47C22⋊(C31⋊C8)C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52(C2×D31)⋊C8C2211yescharacteristic, complemented
53Dic31⋊C8C2211yescharacteristic, complemented
54C8×Dic31C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic, complemented
58#11758396C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31C2311yescharacteristic
61C2×Q8×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31D411yescharacteristic
64C22×Dic31—21no—
65#92499—22no—
66#92499—41no—
67C2×D124—22no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124—21no—
71C2×D124—41no—
72C2×D124C2311yescharacteristic
73C2×D124C2311yescharacteristic
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77Q16×C31—41no—
78C2×C8×C31—41no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C22⋊Dic31D411yescharacteristic
88#92481—22no—
89#92481—41no—
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)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4D411yescharacteristic
105C4×Dic31—21no—
106C4×Dic31—21no—
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C8×D31—41no—
111C23×C31C2×D411yescharacteristic
112C22×D31—21no—
113C22×D31—21no—
114C22×D31—42no—
115C22×D31—42no—
116C22×D31—81no—
117C22×D31C2×D411yescharacteristic
118Q8×C31—21no—
119Q8×C31—21no—
120Q8×C31—21no—
121Q8×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2411yescharacteristic
130C22⋊D31—22no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—42no—
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137D124—21no—
138D124—21no—
139D124—21no—
140D124—42no—
141D124—42no—
142D124—81no—
143D124#4112yes—
144C4×D31—21no—
145C4×D31—21no—
146C4×D31—42no—
147C4×D31—81no—
148C8×C31—21no—
149C8×C31—21no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152#3296—311nomaximal, Sylow
153C22×C31—21no—
154C22×C31—21no—
155C22×C31#13512yes—
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—22no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—84no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31C2×#4111yescharacteristic
173C4×C31H(5,𝔽2)11yescharacteristic
174Dic31—21no—
175Dic31—21no—
176Dic31—21no—
177Dic31—41no—
178Dic31—41no—
179#552—311no—
180#546—311no—
181#488—311no—
182#483—311no—
183#482—311no—
184#478—311no—
185#467D3111yescharacteristic, complemented
186#465—311no—
187#464—311no—
188#452—311no—
189#450—311no—
190C4×SD16—311no—
191C8×D4—311no—
192#416—311no—
193C2×#102—311no—
194C2×C31—22no—
195C2×C31#54611yescharacteristic
196C2×C31C2×#13511yescharacteristic
197C2×C31#57711yescharacteristic
198D31—41no—
199D31—42no—
200D31—81no—
201C2×#41—311no—
202C22×D4—311no—
203C2×Q16C2×D3111yescharacteristic, complemented
204C2×SD16—311no—
205C2×SD16—311no—
206C22×C8—311no—
207C22×C8C2×D3111yescharacteristic
208#126—621no—
209#125—311no—
210#125—621no—
211#124—311no—
212#123—621no—
213#123—621no—
214C22⋊Q8—311no—
215C22⋊Q8C2×D3111yescharacteristic
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#107C2×D3111yescharacteristic, complemented
228#106—311no—
229#106—311no—
230C4⋊C8—311no—
231#103—311no—
232#103—311no—
233#103C2×D3111yescharacteristic, complemented
234#103C2×D3111yescharacteristic, complemented
235#102—311no—
236#102—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241C22⋊C8—311no—
242C22⋊C8—311no—
243C4×C8—311no—
244C31#329611yescharacteristic, complemented, Sylow
245C24—621no—
246#41—622no—
247#41—1241no—
248C2×Q8C22×D3111yescharacteristic
249C2×Q8C22×D3111yescharacteristic
250C2×D4—311no—
251C2×D4—311no—
252C2×D4—311no—
253C2×D4—622no—
254C2×D4—621no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4—1241no—
258C22×C4—311no—
259C22×C4—621no—
260C22×C4—621no—
261C22×C4—621no—
262C22×C4C22×D3111yescharacteristic
263Q16—41no—
264SD16—622no—
265SD16—1241no—
266C2×C8—41no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8—1241no—
270C2×C8C22×D3111yescharacteristic
271C2×C8C22×D3111yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
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⋊C4C22×D3111yescharacteristic
283C4⋊C4C22×D3111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—311no—
287C22⋊C4—311no—
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—311no—
298C23—621no—
299C23—621no—
300C23—1242no—
301C23—1242no—
302C23—2481no—
303C23D4×D3111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—312no—
309D4—622no—
310D4—621no—
311D4—621no—
312D4—621no—
313D4—1242no—
314D4—1242no—
315D4—2481no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—311no—
323C2×C4—311no—
324C2×C4—311no—
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—621no—
341C22—621no—
342C22—622no—
343C22—621no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22—1241no—
348C22—1241no—
349C22—2484no—
350C22#1175849612yes—
351C22C2×D4×D3111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—621no—
358C4—621no—
359C4—621no—
360C4—1241no—
361C4—1241no—
362C4#1175856111yescharacteristic
363C4#41×D3111yescharacteristic
364C2—22no—
365C2—1241no—
366C2—1242no—
367C2—2481no—
368C2#1452168811yescharacteristic
369C2C2×#1175849611yescharacteristic
370C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#467C2
socleC22×C31C22×D4
prime radical#14521690C2
hypercenter#467D31
hypocenterC31#3296
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #14521741C2semidirect
3. #14521405C2semidirect
4. #14521377C2semidirect
5. #14521376C2semidirect
6. #14521352C2semidirect
7. #14521281C2semidirect
8. #14521273C2semidirect
9. #14521210C2semidirect
10. #14521199C2semidirect
11. #14521134C2semidirect
12. C8×C22⋊D31C2semidirect
13. #14521044C2semidirect
14. C2×#11758409C2semidirect
15. C31×#467C2semidirect
18. C2×Q16×C31C22semidirect
23. #11758523C22semidirect
24. Q8×Dic31C22semidirect
29. C2×C8×D31C22semidirect
35. #11758469C22semidirect
37. #11758467C22semidirect
42. C31×#107C22semidirect
43. C31×#103C22semidirect
44. C31×#103C22semidirect
45. #11758423C22semidirect
46. #11758423C22semidirect
52. (C2×D31)⋊C8C22semidirect
53. Dic31⋊C8C22semidirect
54. C8×Dic31C22semidirect
57. #11758396C22semidirect
58. #11758396C22semidirect
185. #467D31semidirect
203. C2×Q16C2×D31semidirect
227. #107C2×D31semidirect
233. #103C2×D31semidirect
234. #103C2×D31semidirect
244. C31#3296semidirect

Maximal subgroups

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

subgroupindex
#145217412
#145216902
#145214052
#145213772
#145213762
#145213522
#145212812
#145212732
#145212102
#145211992
#145211342
C8×C22⋊D312
#145210442
C2×#117584092
C31×#4672
#329631