Finite Group Databasebeta

← #16857789

Subgroups — #16857789

Order 3968.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521760C211yesmaximal, characteristic, complemented
2#14521694C211yesmaximal, characteristic
3#14521411C211yesmaximal, characteristic, complemented
4#14521386C211yesmaximal, characteristic, complemented
5#14521364C211yesmaximal, characteristic, complemented
6#14521296C211yesmaximal, characteristic, complemented
7#14521291C211yesmaximal, characteristic, complemented
8#14521272C211yesmaximal, characteristic, complemented
9#14521212C211yesmaximal, characteristic, complemented
10#14521201C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12#14521119C211yesmaximal, characteristic, complemented
13#14521047C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#474C211yesmaximal, characteristic, complemented
16C2×#92497C2211yescharacteristic
17C2×D4×D31C2211yescharacteristic
18C31×C4⋊Q8C2211yescharacteristic, complemented
19C4×D4×C31C2211yescharacteristic
20#11758523—21no—
21#11758523—21no—
22C2×#92480C2211yescharacteristic
23#11758507—21no—
24C2×(C2×D31)⋊C4—21no—
25C2×Dic124C2211yescharacteristic, complemented
26C2×#92470C2211yescharacteristic
27C2×#92469C2211yescharacteristic, complemented
28C2×C8×D31C2211yescharacteristic
29#11758474C2211yescharacteristic
30#11758474C2211yescharacteristic
31#11758474C2211yescharacteristic, complemented
32#11758472C2211yescharacteristic
33#11758470—21no—
34C4⋊C4×D31C2211yescharacteristic
35C4⋊C4×D31C2211yescharacteristic, complemented
36#11758467—21no—
37#11758463—21no—
38#11758459—21no—
39#11758452C2211yescharacteristic
40C4×D124C2211yescharacteristic
41C4×Dic62C2211yescharacteristic, complemented
42C31×#107C2211yescharacteristic, complemented
43C31×#107C2211yescharacteristic, complemented
44C31×C4⋊C8C2211yescharacteristic, complemented
45C31×#102C2211yescharacteristic
46C31×#102C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic, complemented
51#11758404C2211yescharacteristic, complemented
52#11758398C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758398C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758395C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31—21no—
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×D31—21no—
75C2×C4×D31C2311yescharacteristic
76C2×C4×D31C2311yescharacteristic
77C2×Dic62C2311yescharacteristic
78C2×Dic62C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C42×C31C2311yescharacteristic
87#92480—22no—
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)⋊C4D411yescharacteristic
95(C2×D31)⋊C4D411yescharacteristic
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31D411yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107Dic124—41no—
108#92470—41no—
109#92469—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—81no—
119D4×C31—21no—
120D4×C31#4112yes—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—81no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—42no—
129C22⋊D31—42no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—42no—
134C2×Dic31C2×D411yescharacteristic
135C2×Dic31C2×D411yescharacteristic
136D124—22no—
137D124—21no—
138D124—21no—
139D124—81no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—21no—
144C4×D31—81no—
145C4×D31—81no—
146Dic62—21no—
147Dic62—21no—
148Dic62—21no—
149Dic62—21no—
150C8×C31—21no—
151C8×C31—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154#3314—311nomaximal, Sylow
155C22×C31—22no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31C22×D411yescharacteristic
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—21no—
163C2×D31—21no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—84no—
168C2×D31#13712yes—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31C2×#4111yescharacteristic
175C4×C31H(5,𝔽2)11yescharacteristic
176Dic31—21no—
177Dic31—21no—
178Dic31—41no—
179Dic31—41no—
180Dic31—41no—
181#554—311no—
182#546—311no—
183#489—311no—
184#484—311no—
185#480—311no—
186#474D3111yescharacteristic, complemented
187#468—311no—
188#467—311no—
189#464—311no—
190#452—311no—
191#450—311no—
192#440—311no—
193#435—311no—
194#417—311no—
195C2×#102—311no—
196C2×C31—42no—
197C2×C31#54611yescharacteristic
198C2×C31C2×#13711yescharacteristic
199C2×C31#57611yescharacteristic
200D31—22no—
201D31—41no—
202D31—81no—
203C2×#41—311no—
204C22×D4—311no—
205C2×Q16—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×M16—311no—
209C22×C8—311no—
210C4⋊Q8C2×D3111yescharacteristic, complemented
211#125—621no—
212#124—311no—
213#123—621no—
214C22⋊Q8—311no—
215C22⋊Q8—311no—
216C22⋊Q8—311no—
217C22⋊Q8—621no—
218C22⋊Q8—621no—
219#121—311no—
220#121—621no—
221#120—621no—
222C4×Q8—311no—
223C4×D4—311no—
224C4×D4—621no—
225C4×D4C2×D3111yescharacteristic
226C2×C4⋊C4—311no—
227C2×C4⋊C4—311no—
228C2×C22⋊C4—621no—
229#107—311no—
230#107C2×D3111yescharacteristic, complemented
231#107C2×D3111yescharacteristic, complemented
232C4⋊C8C2×D3111yescharacteristic, complemented
233#103—311no—
234#103—311no—
235#103—311no—
236#103—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241#102C2×D3111yescharacteristic
242#102C2×D3111yescharacteristic
243C22⋊C8—311no—
244C22⋊C8—311no—
245#97—311no—
246C31#331411yescharacteristic, complemented, Sylow
247C24—621no—
248#41—622no—
249#41—1241no—
250C2×Q8—21no—
251C2×Q8—311no—
252C2×Q8—311no—
253C2×D4—311no—
254C2×D4—311no—
255C2×D4—621no—
256C2×D4—621no—
257C2×D4—622no—
258C2×D4—621no—
259C2×D4—1241no—
260C2×D4C22×D3111yescharacteristic
261C22×C4—21no—
262C22×C4—311no—
263C22×C4—311no—
264C22×C4—621no—
265C22×C4—621no—
266C22×C4—621no—
267Q16—1241no—
268SD16—622no—
269SD16—1241no—
270M16—1241no—
271C2×C8—311no—
272C2×C8—311no—
273C2×C8—1241no—
274C2×C8C22×D3111yescharacteristic
275C2×C8C22×D3111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—311no—
278C4⋊C4—311no—
279C4⋊C4—621no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4—621no—
283C4⋊C4—621no—
284C4⋊C4—621no—
285C4⋊C4C22×D3111yescharacteristic
286C4⋊C4C22×D3111yescharacteristic
287C4⋊C4C22×D3111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—311no—
290C22⋊C4—311no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C42—621no—
298C42C22×D3111yescharacteristic
299C23—21no—
300C23—311no—
301C23—311no—
302C23—621no—
303C23—1242no—
304C23—1242no—
305C23—2481no—
306Q8—81no—
307Q8—621no—
308Q8—621no—
309Q8—621no—
310Q8—621no—
311D4—21no—
312D4—622no—
313D4—621no—
314D4—621no—
315D4—1242no—
316D4—1242no—
317D4—2481no—
318D4#9249912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—311no—
324C2×C4—311no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—621no—
332C2×C4—1242no—
333C2×C4—2481no—
334C2×C4—2481no—
335C2×C4D4×D3111yescharacteristic
336C2×C4D4×D3111yescharacteristic
337C2×C4C23×D3111yescharacteristic
338C8—21no—
339C8—21no—
340C8—621no—
341C8—621no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—312no—
346C22—621no—
347C22—621no—
348C22—621no—
349C22—621no—
350C22—621no—
351C22—1241no—
352C22—1241no—
353C22—1241no—
354C22—2484no—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—621no—
362C4—621no—
363C4—1241no—
364C4—1241no—
365C4—1241no—
366C4C2×#9249911yescharacteristic
367C4#1175856611yescharacteristic
368C2—42no—
369C2—622no—
370C2—1241no—
371C2—2481no—
372C2#1452169011yescharacteristic
373C2#137×D3111yescharacteristic
374C2#1452185011yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#474C2
socleC22×C31C22×D4
prime radical#14521694C2
hypercenter#474D31
hypocenterC31#3314
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14521760C2semidirect
3. #14521411C2semidirect
4. #14521386C2semidirect
5. #14521364C2semidirect
6. #14521296C2semidirect
7. #14521291C2semidirect
8. #14521272C2semidirect
9. #14521212C2semidirect
10. #14521201C2semidirect
11. #14521149C2semidirect
12. #14521119C2semidirect
13. #14521047C2semidirect
14. #102×D31C2semidirect
15. C31×#474C2semidirect
18. C31×C4⋊Q8C22semidirect
25. C2×Dic124C22semidirect
27. C2×#92469C22semidirect
31. #11758474C22semidirect
35. C4⋊C4×D31C22semidirect
41. C4×Dic62C22semidirect
42. C31×#107C22semidirect
43. C31×#107C22semidirect
44. C31×C4⋊C8C22semidirect
50. (C2×D31)⋊C8C22semidirect
51. #11758404C22semidirect
52. #11758398C22semidirect
53. #11758398C22semidirect
54. #11758398C22semidirect
57. #11758395C22semidirect
58. #11758391C22semidirect
186. #474D31semidirect
210. C4⋊Q8C2×D31semidirect
230. #107C2×D31semidirect
231. #107C2×D31semidirect
232. C4⋊C8C2×D31semidirect
246. C31#3314semidirect

Maximal subgroups

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

subgroupindex
#145217602
#145216942
#145214112
#145213862
#145213642
#145212962
#145212912
#145212722
#145212122
#145212012
#145211492
#145211192
#145210472
#102×D312
C31×#4742
#331431