Finite Group Databasebeta

← #16855622

Subgroups — #16855622

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#14521556C211yesmaximal, characteristic
2#117×D31C211yesmaximal, characteristic, complemented
3#14521389C211yesmaximal, characteristic, complemented
4#14521388C211yesmaximal, characteristic, complemented
5#14521383C211yesmaximal, characteristic, complemented
6#14521378C211yesmaximal, characteristic, complemented
7#14521372C211yesmaximal, characteristic, complemented
8#14521371C211yesmaximal, characteristic, complemented
9#14521366C211yesmaximal, characteristic, complemented
10#14521361C211yesmaximal, characteristic, complemented
11#14521087C211yesmaximal, characteristic, complemented
12#14521085C211yesmaximal, characteristic, complemented
13#14521045C211yesmaximal, characteristic, complemented
14C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
15C31×#416C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C22×C4×D31C2211yescharacteristic
18C22×C8×C31C2211yescharacteristic
19C31×#117C2211yescharacteristic
20#11758523C2211yescharacteristic
21#11758523C2211yescharacteristic
22#11758515C2211yescharacteristic
23#11758515C2211yescharacteristic
24#11758514—21no—
25#11758512—21no—
26C4×C22⋊D31—21no—
27C4×C22⋊D31—21no—
28#11758503C2211yescharacteristic
29#11758503C2211yescharacteristic
30C22×C31⋊C8C2211yescharacteristic
31#11758469C2211yescharacteristic
32#11758469C2211yescharacteristic
33C4⋊C4×D31C2211yescharacteristic
34C4⋊C4×D31C2211yescharacteristic
35C22⋊C4×D31—21no—
36#11758454—21no—
37#11758449—21no—
38C42×D31—21no—
39C31×#103C2211yescharacteristic, complemented
40C31×#103C2211yescharacteristic, complemented
41C31×#102C2211yescharacteristic, complemented
42C31×#102C2211yescharacteristic, complemented
43#11758423C2211yescharacteristic, complemented
44#11758423C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic, complemented
47(C2×D31)⋊C8C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758406C2211yescharacteristic, complemented
52#11758406C2211yescharacteristic, complemented
53#11758405C2211yescharacteristic, complemented
54#11758405C2211yescharacteristic, complemented
55#11758396C2211yescharacteristic, complemented
56#11758396C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C23×D31D411yescharacteristic
60#41×C31—22no—
61#41×C31—22no—
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31—21no—
64C2×D4×C31C2311yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C22×Dic31D411yescharacteristic
70C2×C4×D31—22no—
71C2×C4×D31—22no—
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×C4×D31D411yescharacteristic
75C2×C4×D31D411yescharacteristic
76C2×C4×D31C2311yescharacteristic
77C2×C4×D31C2311yescharacteristic
78C2×C8×C31—22no—
79C2×C8×C31C2311yescharacteristic
80C2×C8×C31C2311yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C42×C31—21no—
85C22⋊Dic31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93C4⋊Dic31C2311yescharacteristic
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101C4×Dic31—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31—21no—
105C2×C31⋊C8—22no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—21no—
109C23×C31C2×D411yescharacteristic
110C22×D31—22no—
111C22×D31—22no—
112C22×D31—41no—
113C22×D31C2×D411yescharacteristic
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31—21no—
117D4×C31—21no—
118D4×C31—21no—
119D4×C31—42no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—42no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31#4112yes—
126C2×C4×C31#4112yes—
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—42no—
129C22⋊D31—42no—
130C2×Dic31—22no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31C2×D411yescharacteristic
136C2×Dic31C2×D411yescharacteristic
137C4×D31—22no—
138C4×D31—22no—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—42no—
144C4×D31—42no—
145C8×C31—21no—
146C8×C31—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3091—311nomaximal, Sylow
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31#12312yes—
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—44no—
163C2×D31#13512yes—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31#12312yes—
168C4×C31C2×#4111yescharacteristic
169C4×C31C2×#4111yescharacteristic
170Dic31—21no—
171Dic31—21no—
172Dic31—41no—
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#427—311no—
188#416—311no—
189#416D3111yescharacteristic, complemented
190C2×C22⋊C8—311no—
191C2×C31—22no—
192C2×C31—81no—
193C2×C31C2×#12311yescharacteristic
194C2×C31C2×#13511yescharacteristic
195C2×C31#57511yescharacteristic
196D31—22no—
197D31—41no—
198C2×#41C2×D3111yescharacteristic
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—311no—
214#117—621no—
215#117—621no—
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#107—311no—
224#107—311no—
225#106—311no—
226#106—311no—
227#106—311no—
228#106—311no—
229#103—311no—
230#103—311no—
231#103C2×D3111yescharacteristic, complemented
232#103C2×D3111yescharacteristic, complemented
233#102—311no—
234#102—311no—
235#102C2×D3111yescharacteristic, complemented
236#102C2×D3111yescharacteristic, complemented
237C22⋊C8—311no—
238C22⋊C8—311no—
239C22⋊C8—311no—
240C22⋊C8—311no—
241C31#309111yescharacteristic, complemented, Sylow
242C24—311no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D3111yescharacteristic
246C2×D4—21no—
247C2×D4—621no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C22×C4—21no—
251C22×C4—311no—
252C22×C4—311no—
253C22×C4—311no—
254C22×C4—311no—
255C22×C4—311no—
256C22×C4—621no—
257C22×C4—621no—
258C22×C4—622no—
259C22×C4—622no—
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—311no—
270C4⋊C4—311no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4C22×D3111yescharacteristic
276C4⋊C4C22×D3111yescharacteristic
277C22⋊C4—21no—
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—621no—
288C42—621no—
289C42—621no—
290C42—621no—
291C23—21no—
292C23—311no—
293C23—311no—
294C23—622no—
295C23—622no—
296C23—1241no—
297C23D4×D3111yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—1242no—
304D4—1242no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
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—621no—
322C2×C4—1242no—
323C2×C4—1242no—
324C2×C4#9249512yes—
325C2×C4D4×D3111yescharacteristic
326C2×C4#9249712yes—
327C2×C4C23×D3111yescharacteristic
328C8—21no—
329C8—21no—
330C8—621no—
331C8—621no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—312no—
338C22—621no—
339C22—621no—
340C22—621no—
341C22—621no—
342C22—621no—
343C22—1244no—
344C22#1175846012yes—
345C22C2×D4×D3111yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—621no—
350C4—621no—
351C4—1241no—
352C4—1241no—
353C4—1241no—
354C4—1241no—
355C4#1175846012yes—
356C4C2×#9249511yescharacteristic
357C4C2×#9249711yescharacteristic
358C2—22no—
359C2—81no—
360C2—622no—
361C2—1241no—
362C2C2×#1175846011yescharacteristic
363C2#135×D3111yescharacteristic
364C2#1452184611yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#416C2
socleC22×C31C22×D4
prime radical#14521556C2
hypercenter#416D31
hypocenterC31#3091
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D31C2semidirect
3. #14521389C2semidirect
4. #14521388C2semidirect
5. #14521383C2semidirect
6. #14521378C2semidirect
7. #14521372C2semidirect
8. #14521371C2semidirect
9. #14521366C2semidirect
10. #14521361C2semidirect
11. #14521087C2semidirect
12. #14521085C2semidirect
13. #14521045C2semidirect
14. C2×(C2×D31)⋊C8C2semidirect
15. C31×#416C2semidirect
39. C31×#103C22semidirect
40. C31×#103C22semidirect
41. C31×#102C22semidirect
42. C31×#102C22semidirect
43. #11758423C22semidirect
44. #11758423C22semidirect
45. #11758420C22semidirect
46. #11758420C22semidirect
51. #11758406C22semidirect
52. #11758406C22semidirect
53. #11758405C22semidirect
54. #11758405C22semidirect
55. #11758396C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. #11758395C22semidirect
189. #416D31semidirect
231. #103C2×D31semidirect
232. #103C2×D31semidirect
235. #102C2×D31semidirect
236. #102C2×D31semidirect
241. C31#3091semidirect

Maximal subgroups

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

subgroupindex
#145215562
#117×D312
#145213892
#145213882
#145213832
#145213782
#145213722
#145213712
#145213662
#145213612
#145210872
#145210852
#145210452
C2×(C2×D31)⋊C82
C31×#4162
#309131