Finite Group Databasebeta

← #16855890

Subgroups — #16855890

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#14521666C211yesmaximal, characteristic, complemented
2#14521523C211yesmaximal, characteristic, complemented
3#14521390C211yesmaximal, characteristic, complemented
4#14521338C211yesmaximal, characteristic, complemented
5#14521328C211yesmaximal, characteristic, complemented
6#14521263C211yesmaximal, characteristic, complemented
7#14521263C211yesmaximal, characteristic, complemented
8#14521202C211yesmaximal, characteristic, complemented
9#14521182C211yesmaximal, characteristic
10#14521158C211yesmaximal, characteristic, complemented
11#14521148C211yesmaximal, characteristic, complemented
12#14521136C211yesmaximal, characteristic, complemented
13#14521129C211yesmaximal, characteristic, complemented
14#14521107C211yesmaximal, characteristic, complemented
15C31×#482C211yesmaximal, characteristic, complemented
16C22×D124C2211yescharacteristic
17C31×#121C2211yescharacteristic
18C31×#117C2211yescharacteristic
19#11758513—21no—
20#11758513C2211yescharacteristic, complemented
21#11758512—21no—
22D4×Dic31C2211yescharacteristic, complemented
23C2×#92479C2211yescharacteristic
24C2×#92479C2211yescharacteristic
25#11758503C2211yescharacteristic
26#11758501C2211yescharacteristic
27C2×#92470C2211yescharacteristic
28C2×#92470C2211yescharacteristic
29#11758470C2211yescharacteristic
30#11758470C2211yescharacteristic
31#11758470C2211yescharacteristic
32#11758470C2211yescharacteristic
33#11758465C2211yescharacteristic, complemented
34#11758464C2211yescharacteristic, complemented
35C22⋊C4×D31—21no—
36C22⋊C4×D31—21no—
37#11758456—21no—
38#11758455—21no—
39C4×D124—21no—
40C4×D124—21no—
41C31×#107C2211yescharacteristic, complemented
42C31×#106C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic, complemented
44C31×#102C2211yescharacteristic, complemented
45C31×C22⋊C8C2211yescharacteristic
46C22⋊(C31⋊C8)C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758403C2211yescharacteristic, complemented
50Dic31⋊C8C2211yescharacteristic, complemented
51Dic31⋊C8C2211yescharacteristic, complemented
52C8×Dic31C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758398C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758396C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×D4×C31—21no—
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C22×Dic31—21no—
64C2×D124—21no—
65C2×D124—22no—
66C2×D124—22no—
67C2×D124C2311yescharacteristic
68C2×D124C2311yescharacteristic
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
77C4⋊C4×C31C2311yescharacteristic
78C4⋊C4×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C42×C31—21no—
83C22⋊Dic31—21no—
84C22⋊Dic31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31D411yescharacteristic
88C22⋊Dic31D411yescharacteristic
89#92479—22no—
90#92479—22no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95C4⋊Dic31D411yescharacteristic
96C4⋊Dic31D411yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101C4×Dic31—21no—
102C4×Dic31C2311yescharacteristic
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106#92470—22no—
107#92470—22no—
108C23×C31—21no—
109C23×C31C2×D411yescharacteristic
110C22×D31—21no—
111C22×D31—21no—
112C22×D31—24no—
113C22×D31—81no—
114C22×D31—81no—
115D4×C31—21no—
116D4×C31—21no—
117D4×C31—81no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—81no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132D124—24no—
133D124—21no—
134D124—21no—
135D124#4112yes—
136D124#4112yes—
137C4×D31—81no—
138C4×D31—81no—
139C4×D31—81no—
140C4×D31—81no—
141Dic62—21no—
142Dic62—21no—
143Dic62—81no—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3118—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—22no—
157C2×D31—22no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—84no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31C2×#4111yescharacteristic
168C4×C31C2×#4111yescharacteristic
169Dic31—21no—
170Dic31—21no—
171Dic31—21no—
172Dic31—21no—
173Dic31—41no—
174Dic31—41no—
175#542—311no—
176#518—311no—
177#485—311no—
178#482D3111yescharacteristic, complemented
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#433—311no—
190C2×C31—41no—
191C2×C31—81no—
192C2×C31#52511yescharacteristic
193C2×C31#57611yescharacteristic
194C2×C31#57711yescharacteristic
195D31—42no—
196D31—42no—
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#121C2×D3111yescharacteristic
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#107C2×D3111yescharacteristic, complemented
224#106—311no—
225#106C2×D3111yescharacteristic, complemented
226C4⋊C8—311no—
227C4⋊C8—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102C2×D3111yescharacteristic, complemented
235#102C2×D3111yescharacteristic, complemented
236C22⋊C8—311no—
237C22⋊C8C2×D3111yescharacteristic
238#97—311no—
239C4×C8—311no—
240C31#311811yescharacteristic, complemented, Sylow
241C24—621no—
242C2×Q8—311no—
243C2×Q8—621no—
244C2×D4—21no—
245C2×D4—311no—
246C2×D4—311no—
247C2×D4—622no—
248C2×D4—622no—
249C2×D4—621no—
250C2×D4C22×D3111yescharacteristic
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×C8—311no—
262C2×C8—311no—
263C2×C8C22×D3111yescharacteristic
264C2×C8C22×D3111yescharacteristic
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4C22×D3111yescharacteristic
272C4⋊C4C22×D3111yescharacteristic
273C4⋊C4C22×D3111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—311no—
277C22⋊C4—311no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C42—21no—
287C42—311no—
288C42—311no—
289C42—621no—
290C23—21no—
291C23—624no—
292C23—621no—
293C23—621no—
294C23—2481no—
295C23—2481no—
296C23D4×D3111yescharacteristic
297Q8—621no—
298Q8—621no—
299Q8—2481no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—312no—
304D4—312no—
305D4—624no—
306D4—621no—
307D4—621no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—311no—
314C2×C4—311no—
315C2×C4—311no—
316C2×C4—311no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4—2481no—
323C2×C4—2481no—
324C2×C4D4×D3111yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—21no—
327C8—21no—
328C8—621no—
329C8—621no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—622no—
337C22—622no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22—1241no—
342C22—2484no—
343C22C2×D4×D3111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—621no—
349C4—621no—
350C4—621no—
351C4—621no—
352C4—1241no—
353C4—1241no—
354C4#41×D3111yescharacteristic
355C4#41×D3111yescharacteristic
356C2—41no—
357C2—81no—
358C2—1242no—
359C2—1242no—
360C2#1452155711yescharacteristic
361C2#1452185311yescharacteristic
362C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#482C2
socleC22×C31C22×D4
prime radical#14521182C2
hypercenter#482D31
hypocenterC31#3118
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14521666C2semidirect
2. #14521523C2semidirect
3. #14521390C2semidirect
4. #14521338C2semidirect
5. #14521328C2semidirect
6. #14521263C2semidirect
7. #14521263C2semidirect
8. #14521202C2semidirect
10. #14521158C2semidirect
11. #14521148C2semidirect
12. #14521136C2semidirect
13. #14521129C2semidirect
14. #14521107C2semidirect
15. C31×#482C2semidirect
20. #11758513C22semidirect
22. D4×Dic31C22semidirect
33. #11758465C22semidirect
34. #11758464C22semidirect
41. C31×#107C22semidirect
42. C31×#106C22semidirect
43. C31×#102C22semidirect
44. C31×#102C22semidirect
49. #11758403C22semidirect
50. Dic31⋊C8C22semidirect
51. Dic31⋊C8C22semidirect
52. C8×Dic31C22semidirect
53. #11758398C22semidirect
54. #11758398C22semidirect
57. #11758396C22semidirect
58. #11758395C22semidirect
178. #482D31semidirect
223. #107C2×D31semidirect
225. #106C2×D31semidirect
234. #102C2×D31semidirect
235. #102C2×D31semidirect
240. C31#3118semidirect

Maximal subgroups

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

subgroupindex
#145216662
#145215232
#145213902
#145213382
#145213282
#145212632
#145212022
#145211822
#145211582
#145211482
#145211362
#145211292
#145211072
C31×#4822
#311831