Finite Group Databasebeta

← #16855628

Subgroups — #16855628

Order 3968.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521561C211yesmaximal, characteristic
2#117×D31C211yesmaximal, characteristic, complemented
3#14521393C211yesmaximal, characteristic, complemented
4#14521392C211yesmaximal, characteristic, complemented
5#14521386C211yesmaximal, characteristic, complemented
6#14521381C211yesmaximal, characteristic, complemented
7#14521376C211yesmaximal, characteristic, complemented
8#14521375C211yesmaximal, characteristic, complemented
9#14521369C211yesmaximal, characteristic, complemented
10#14521364C211yesmaximal, characteristic, complemented
11#14521085C211yesmaximal, characteristic, complemented
12#14521046C211yesmaximal, characteristic, complemented
13#14521043C211yesmaximal, characteristic, complemented
14C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
15C31×#427C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C22×C4×D31C2211yescharacteristic
18C22×C8×C31C2211yescharacteristic
19C31×#117C2211yescharacteristic
20C31×#117C2211yescharacteristic
21#11758503C2211yescharacteristic
22C22×C31⋊C8C2211yescharacteristic
23#11758474C2211yescharacteristic
24#11758474C2211yescharacteristic
25#11758472C2211yescharacteristic
26#11758472C2211yescharacteristic
27#11758469C2211yescharacteristic
28#11758469C2211yescharacteristic
29C4⋊C4×D31C2211yescharacteristic
30C4⋊C4×D31C2211yescharacteristic
31#11758463—21no—
32#11758459—21no—
33C22⋊C4×D31—21no—
34#11758454—21no—
35C4×D124—21no—
36C4×D124—21no—
37#11758449—21no—
38C42×D31—21no—
39C31×#107C2211yescharacteristic, complemented
40C31×#107C2211yescharacteristic, complemented
41C31×#106C2211yescharacteristic, complemented
42C31×#106C2211yescharacteristic, complemented
43#11758409C2211yescharacteristic, complemented
44#11758409C2211yescharacteristic, complemented
45(C2×D31)⋊C8C2211yescharacteristic
46(C2×D31)⋊C8C2211yescharacteristic
47(C2×D31)⋊C8C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49#11758404C2211yescharacteristic, complemented
50#11758404C2211yescharacteristic, complemented
51#11758398C2211yescharacteristic, complemented
52#11758398C2211yescharacteristic, complemented
53#11758397C2211yescharacteristic, complemented
54#11758397C2211yescharacteristic, complemented
55#11758396C2211yescharacteristic, complemented
56#11758396C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C23×D31D411yescharacteristic
60C22×C4×C31C2311yescharacteristic
61C2×C22⋊D31—21no—
62C22×Dic31D411yescharacteristic
63#92495—22no—
64#92495—22no—
65C2×D124—21no—
66C2×D124—21no—
67C2×D124C2311yescharacteristic
68C2×C4×D31—22no—
69C2×C4×D31—22no—
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31D411yescharacteristic
74C2×C4×D31D411yescharacteristic
75C2×C4×D31C2311yescharacteristic
76C2×C4×D31C2311yescharacteristic
77C2×Dic62C2311yescharacteristic
78C2×C8×C31—22no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C42×C31—21no—
88C42×C31—21no—
89C22⋊Dic31—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)⋊C4—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31—21no—
105C2×C31⋊C8—22no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31C2×D411yescharacteristic
109C22×D31—22no—
110C22×D31—22no—
111C22×D31—21no—
112C22×D31—41no—
113C22×D31C2×D411yescharacteristic
114C22×D31C2×D411yescharacteristic
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31C2×D411yescharacteristic
120C2×C4×C31#4112yes—
121C2×C4×C31#4112yes—
122C2×C4×C31C2411yescharacteristic
123C22⋊D31—42no—
124C2×Dic31—22no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130D124—21no—
131D124—21no—
132D124—42no—
133D124—42no—
134C4×D31—22no—
135C4×D31—22no—
136C4×D31—21no—
137C4×D31—21no—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—42no—
141C4×D31—42no—
142C4×D31—42no—
143Dic62—21no—
144Dic62—21no—
145C8×C31—21no—
146C8×C31—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3091—311nomaximal, Sylow
150C22×C31—21no—
151C22×C31—21no—
152C22×C31#12312yes—
153C22×C31C22×D411yescharacteristic
154C2×D31—21no—
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—44no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31#13512yes—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31#12312yes—
169C4×C31C2×#4111yescharacteristic
170C4×C31C2×#4111yescharacteristic
171Dic31—21no—
172Dic31—21no—
173Dic31—41no—
174Dic31—41no—
175Dic31—41no—
176#525—311no—
177C2×#117—311no—
178#485—311no—
179#485—311no—
180#484—311no—
181#483—311no—
182#482—311no—
183#482—311no—
184#481—311no—
185#480—311no—
186#427—311no—
187#427D3111yescharacteristic, complemented
188#416—311no—
189#416—311no—
190C2×C22⋊C8—311no—
191C2×C31—22no—
192C2×C31C2×#12311yescharacteristic
193C2×C31C2×#13511yescharacteristic
194C2×C31#57511yescharacteristic
195D31—22no—
196D31—41no—
197D31—81no—
198C2×#41—311no—
199C23×C4—311no—
200C22×C8—311no—
201C22×C8C2×D3111yescharacteristic
202#123—621no—
203C22⋊Q8—311no—
204C22⋊Q8—311no—
205#121—311no—
206#121—311no—
207#120—621no—
208C4×D4—621no—
209C4×D4—621no—
210#117—311no—
211#117—311no—
212#117—311no—
213#117—621no—
214#117—621no—
215#117C2×D3111yescharacteristic
216#117C2×D3111yescharacteristic
217C2×C4⋊C4—311no—
218C2×C4⋊C4—311no—
219C2×C22⋊C4—621no—
220C2×C42—621no—
221#107—311no—
222#107—311no—
223#107C2×D3111yescharacteristic, complemented
224#107C2×D3111yescharacteristic, complemented
225#106—311no—
226#106—311no—
227#106C2×D3111yescharacteristic, complemented
228#106C2×D3111yescharacteristic, complemented
229#103—311no—
230#103—311no—
231#103—311no—
232#103—311no—
233#102—311no—
234#102—311no—
235#102—311no—
236#102—311no—
237C22⋊C8—311no—
238C22⋊C8—311no—
239C22⋊C8—311no—
240C22⋊C8—311no—
241C31#309111yescharacteristic, complemented, Sylow
242C24—311no—
243#41—622no—
244#41—622no—
245C2×Q8—311no—
246C2×D4—311no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4—621no—
250C22×C4—311no—
251C22×C4—311no—
252C22×C4—311no—
253C22×C4—311no—
254C22×C4—311no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—622no—
258C22×C4—622no—
259C22×C4—621no—
260C22×C4C22×D3111yescharacteristic
261C2×C8—22no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8—622no—
265C2×C8C22×D3111yescharacteristic
266C2×C8C22×D3111yescharacteristic
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4C22×D3111yescharacteristic
274C4⋊C4C22×D3111yescharacteristic
275C4⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C42—21no—
287C42—21no—
288C42—621no—
289C42—621no—
290C42—621no—
291C23—311no—
292C23—311no—
293C23—622no—
294C23—622no—
295C23—621no—
296C23—1241no—
297C23D4×D3111yescharacteristic
298Q8—621no—
299Q8—621no—
300D4—621no—
301D4—621no—
302D4—1242no—
303D4—1242no—
304D4—1242no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—311no—
310C2×C4—311no—
311C2×C4—622no—
312C2×C4—622no—
313C2×C4—622no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—1242no—
322C2×C4—1242no—
323C2×C4—1242no—
324C2×C4#9249512yes—
325C2×C4D4×D3111yescharacteristic
326C2×C4#9249912yes—
327C2×C4C23×D3111yescharacteristic
328C8—21no—
329C8—21no—
330C8—621no—
331C8—621no—
332C22—21no—
333C22—21no—
334C22—312no—
335C22—621no—
336C22—621no—
337C22—621no—
338C22—621no—
339C22—621no—
340C22—1244no—
341C22—1241no—
342C22—1241no—
343C22—1241no—
344C22#1175847112yes—
345C22C2×D4×D3111yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—621no—
351C4—621no—
352C4—1241no—
353C4—1241no—
354C4—1241no—
355C4#1175847112yes—
356C4C2×#9249511yescharacteristic
357C4C2×#9249911yescharacteristic
358C2—22no—
359C2—622no—
360C2—1241no—
361C2—2481no—
362C2C2×#1175847111yescharacteristic
363C2#135×D3111yescharacteristic
364C2#1452184611yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#427C2
socleC22×C31C22×D4
prime radical#14521561C2
hypercenter#427D31
hypocenterC31#3091
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #117×D31C2semidirect
3. #14521393C2semidirect
4. #14521392C2semidirect
5. #14521386C2semidirect
6. #14521381C2semidirect
7. #14521376C2semidirect
8. #14521375C2semidirect
9. #14521369C2semidirect
10. #14521364C2semidirect
11. #14521085C2semidirect
12. #14521046C2semidirect
13. #14521043C2semidirect
14. C2×(C2×D31)⋊C8C2semidirect
15. C31×#427C2semidirect
39. C31×#107C22semidirect
40. C31×#107C22semidirect
41. C31×#106C22semidirect
42. C31×#106C22semidirect
43. #11758409C22semidirect
44. #11758409C22semidirect
49. #11758404C22semidirect
50. #11758404C22semidirect
51. #11758398C22semidirect
52. #11758398C22semidirect
53. #11758397C22semidirect
54. #11758397C22semidirect
55. #11758396C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. #11758395C22semidirect
187. #427D31semidirect
223. #107C2×D31semidirect
224. #107C2×D31semidirect
227. #106C2×D31semidirect
228. #106C2×D31semidirect
241. C31#3091semidirect

Maximal subgroups

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

subgroupindex
#145215612
#117×D312
#145213932
#145213922
#145213862
#145213812
#145213762
#145213752
#145213692
#145213642
#145210852
#145210462
#145210432
C2×(C2×D31)⋊C82
C31×#4272
#309131