Finite Group Databasebeta

← #16857790

Subgroups — #16857790

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#14521754C211yesmaximal, characteristic, complemented
2#14521690C211yesmaximal, characteristic
3#14521410C211yesmaximal, characteristic, complemented
4#14521364C211yesmaximal, characteristic, complemented
5#14521328C211yesmaximal, characteristic, complemented
6#14521296C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521274C211yesmaximal, characteristic, complemented
9#14521214C211yesmaximal, characteristic, complemented
10#14521202C211yesmaximal, characteristic, complemented
11#14521148C211yesmaximal, characteristic, complemented
12#14521117C211yesmaximal, characteristic, complemented
13#14521049C211yesmaximal, characteristic, complemented
14C2×#11758397C211yesmaximal, characteristic, complemented
15C31×#484C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C22×D124C2211yescharacteristic
18C31×C22⋊Q8C2211yescharacteristic
19C2×C4⋊C4×C31C2211yescharacteristic
20#11758524C2211yescharacteristic
21C2×#92482C2211yescharacteristic, complemented
22C4×C22⋊D31—21no—
23C4×C22⋊D31C2211yescharacteristic
24#11758501—21no—
25#11758501C2211yescharacteristic
26C22×C31⋊C8C2211yescharacteristic
27C2×#92470C2211yescharacteristic
28C2×#92470C2211yescharacteristic
29C2×#92469C2211yescharacteristic, complemented
30#11758474C2211yescharacteristic, complemented
31#11758473—21no—
32#11758472—21no—
33#11758472C2211yescharacteristic
34#11758471—21no—
35#11758470C2211yescharacteristic
36C4⋊C4×D31C2211yescharacteristic, complemented
37#11758466—21no—
38#11758465C2211yescharacteristic, complemented
39#11758464C2211yescharacteristic, complemented
40#11758459—21no—
41C22⋊C4×D31—21no—
42C31×#107C2211yescharacteristic, complemented
43C31×#107C2211yescharacteristic, complemented
44C31×#103C2211yescharacteristic, complemented
45C31×#103C2211yescharacteristic, complemented
46C31×C22⋊C8C2211yescharacteristic
47#11758423C2211yescharacteristic, complemented
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic, complemented
51#11758403C2211yescharacteristic, complemented
52Dic31⋊C8C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758397C2211yescharacteristic
58#11758395C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31D411yescharacteristic
64#92499—22no—
65#92499—41no—
66C2×D124—22no—
67C2×D124—21no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124—41no—
71C2×D124C2311yescharacteristic
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31C2311yescharacteristic
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31—21no—
82C4⋊C4×C31—21no—
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C4⋊C4×C31C2311yescharacteristic
86C22⋊C4×C31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31D411yescharacteristic
89#92482—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)⋊C4D411yescharacteristic
96C4⋊Dic31—21no—
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8—41no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108#92470—22no—
109#92470—41no—
110#92469—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—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—81no—
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2411yescharacteristic
129C22⋊D31—22no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135D124—21no—
136D124—21no—
137D124—21no—
138D124—42no—
139D124—42no—
140D124—81no—
141D124#4112yes—
142C4×D31—21no—
143C4×D31—21no—
144C4×D31—42no—
145C4×D31—81no—
146C4×D31—81no—
147Dic62—21no—
148Dic62—21no—
149Dic62—81no—
150C8×C31—21no—
151C8×C31—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154#3314—311nomaximal, Sylow
155C22×C31—21no—
156C22×C31—21no—
157C22×C31#13712yes—
158C22×C31C22×D411yescharacteristic
159C2×D31—21no—
160C2×D31—22no—
161C2×D31—21no—
162C2×D31—21no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—84no—
169C4×C31—21no—
170C4×C31—41no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31C2×#4111yescharacteristic
175C4×C31H(5,𝔽2)11yescharacteristic
176Dic31—21no—
177Dic31—21no—
178Dic31—21no—
179Dic31—41no—
180Dic31—41no—
181#554—311no—
182#546—311no—
183#489—311no—
184#484D3111yescharacteristic, complemented
185#480—311no—
186#474—311no—
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—22no—
197C2×C31#54611yescharacteristic
198C2×C31C2×#13711yescharacteristic
199C2×C31#57611yescharacteristic
200D31—41no—
201D31—42no—
202D31—81no—
203C2×#41—311no—
204C22×D4—311no—
205C2×Q16—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×M16—311no—
209C22×C8—311no—
210C4⋊Q8—311no—
211#125—621no—
212#124—311no—
213#123—621no—
214C22⋊Q8—311no—
215C22⋊Q8—311no—
216C22⋊Q8—621no—
217C22⋊Q8—621no—
218C22⋊Q8C2×D3111yescharacteristic
219#121—311no—
220#121—621no—
221#120—621no—
222C4×Q8—311no—
223C4×D4—311no—
224C4×D4—311no—
225C4×D4—621no—
226C2×C4⋊C4—311no—
227C2×C4⋊C4C2×D3111yescharacteristic
228C2×C22⋊C4—621no—
229#107—311no—
230#107C2×D3111yescharacteristic, complemented
231#107C2×D3111yescharacteristic, complemented
232C4⋊C8—311no—
233#103—311no—
234#103—311no—
235#103C2×D3111yescharacteristic, complemented
236#103C2×D3111yescharacteristic, complemented
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243C22⋊C8—311no—
244C22⋊C8C2×D3111yescharacteristic
245#97—311no—
246C31#331411yescharacteristic, complemented, Sylow
247C24—621no—
248#41—622no—
249#41—1241no—
250C2×Q8—311no—
251C2×Q8—621no—
252C2×Q8C22×D3111yescharacteristic
253C2×D4—311no—
254C2×D4—311no—
255C2×D4—311no—
256C2×D4—622no—
257C2×D4—621no—
258C2×D4—621no—
259C2×D4—621no—
260C2×D4—1241no—
261C22×C4—21no—
262C22×C4—311no—
263C22×C4—621no—
264C22×C4—621no—
265C22×C4—621no—
266C22×C4C22×D3111yescharacteristic
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—21no—
278C4⋊C4—311no—
279C4⋊C4—311no—
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—311no—
298C42—621no—
299C23—311no—
300C23—621no—
301C23—621no—
302C23—1242no—
303C23—1242no—
304C23—2481no—
305C23D4×D3111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—621no—
309Q8—621no—
310Q8—2481no—
311D4—312no—
312D4—622no—
313D4—621no—
314D4—621no—
315D4—621no—
316D4—1242no—
317D4—1242no—
318D4—2481no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—81no—
326C2×C4—311no—
327C2×C4—311no—
328C2×C4—311no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—621no—
332C2×C4—621no—
333C2×C4—1242no—
334C2×C4—2481no—
335C2×C4—2481no—
336C2×C4D4×D3111yescharacteristic
337C2×C4C23×D3111yescharacteristic
338C8—21no—
339C8—21no—
340C8—621no—
341C8—621no—
342C22—21no—
343C22—21no—
344C22—621no—
345C22—622no—
346C22—621no—
347C22—621no—
348C22—1241no—
349C22—1241no—
350C22—1241no—
351C22—1241no—
352C22—1241no—
353C22—2484no—
354C22#1175849512yes—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—621no—
362C4—621no—
363C4—621no—
364C4—1241no—
365C4—1241no—
366C4#41×D3111yescharacteristic
367C4#1175856611yescharacteristic
368C2—22no—
369C2—1241no—
370C2—1242no—
371C2—2481no—
372C2#1452169111yescharacteristic
373C2C2×#1175849511yescharacteristic
374C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#484C2
socleC22×C31C22×D4
prime radical#14521690C2
hypercenter#484D31
hypocenterC31#3314
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #14521754C2semidirect
3. #14521410C2semidirect
4. #14521364C2semidirect
5. #14521328C2semidirect
6. #14521296C2semidirect
7. #14521288C2semidirect
8. #14521274C2semidirect
9. #14521214C2semidirect
10. #14521202C2semidirect
11. #14521148C2semidirect
12. #14521117C2semidirect
13. #14521049C2semidirect
14. C2×#11758397C2semidirect
15. C31×#484C2semidirect
21. C2×#92482C22semidirect
29. C2×#92469C22semidirect
30. #11758474C22semidirect
36. C4⋊C4×D31C22semidirect
38. #11758465C22semidirect
39. #11758464C22semidirect
42. C31×#107C22semidirect
43. C31×#107C22semidirect
44. C31×#103C22semidirect
45. C31×#103C22semidirect
47. #11758423C22semidirect
50. (C2×D31)⋊C8C22semidirect
51. #11758403C22semidirect
52. Dic31⋊C8C22semidirect
53. #11758398C22semidirect
58. #11758395C22semidirect
184. #484D31semidirect
230. #107C2×D31semidirect
231. #107C2×D31semidirect
235. #103C2×D31semidirect
236. #103C2×D31semidirect
246. C31#3314semidirect

Maximal subgroups

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

subgroupindex
#145217542
#145216902
#145214102
#145213642
#145213282
#145212962
#145212882
#145212742
#145212142
#145212022
#145211482
#145211172
#145210492
C2×#117583972
C31×#4842
#331431