Finite Group Databasebeta

← #16857528

Subgroups — #16857528

Order 3968.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521757C211yesmaximal, characteristic, complemented
2D4×C22⋊D31C211yesmaximal, characteristic
3#14521394C211yesmaximal, characteristic, complemented
4#14521368C211yesmaximal, characteristic, complemented
5#14521366C211yesmaximal, characteristic, complemented
6#14521337C211yesmaximal, characteristic, complemented
7#14521280C211yesmaximal, characteristic, complemented
8#14521275C211yesmaximal, characteristic, complemented
9#14521247C211yesmaximal, characteristic, complemented
10#14521198C211yesmaximal, characteristic, complemented
11SD16×Dic31C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
13C2×#11758420C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#450C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C22×C22⋊D31—21no—
18C2×D4×D31C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic
20C2×SD16×C31C2211yescharacteristic, complemented
21C31×C22⋊Q8C2211yescharacteristic, complemented
22#11758530—21no—
23#11758523C2211yescharacteristic, complemented
24Q8×Dic31C2211yescharacteristic, complemented
25C2×#92481C2211yescharacteristic, complemented
26#11758517C2211yescharacteristic
27#11758516—21no—
28#11758515C2211yescharacteristic
29#11758514—21no—
30D4×Dic31C2211yescharacteristic
31#11758507C2211yescharacteristic
32C4×C22⋊D31C2211yescharacteristic
33C2×C4⋊Dic31C2211yescharacteristic, complemented
34C22×C31⋊C8C2211yescharacteristic, complemented
35C2×C8×D31C2211yescharacteristic, complemented
36#11758474—21no—
37C4⋊C4×D31C2211yescharacteristic, complemented
38#11758466—21no—
39#11758465C2211yescharacteristic, complemented
40(C22⋊D31)⋊C4—21no—
41#11758455—21no—
42C31×#102C2211yescharacteristic
43C31×#102C2211yescharacteristic, complemented
44C31×C22⋊C8C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic, complemented
49#11758420C2211yescharacteristic, complemented
50#11758409C2211yescharacteristic, complemented
51#11758409C2211yescharacteristic, complemented
52(C2×D31)⋊C8C2211yescharacteristic, complemented
53#11758405C2211yescharacteristic, complemented
54#11758405C2211yescharacteristic, complemented
55Dic31⋊C8C2211yescharacteristic, complemented
56C8×Dic31C2211yescharacteristic, complemented
57#11758397C2211yescharacteristic, complemented
58#11758396C2211yescharacteristic, complemented
59C24×C31—21no—
60C23×D31—21no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—22no—
63C2×D4×C31—21no—
64C2×D4×C31—41no—
65C2×D4×C31C2311yescharacteristic
66C2×D4×C31C2311yescharacteristic
67C22×C4×C31C2311yescharacteristic
68C2×C22⋊D31—21no—
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31—21no—
73C2×C22⋊D31—44no—
74C2×C22⋊D31D411yescharacteristic
75C22×Dic31—21no—
76C22×Dic31—21no—
77D4×D31—22no—
78D4×D31—41no—
79C2×D124C2311yescharacteristic
80C2×C4×D31—21no—
81C2×C4×D31C2311yescharacteristic
82C2×Dic62—21no—
83SD16×C31—22no—
84SD16×C31—41no—
85C2×C8×C31C2311yescharacteristic
86C2×C8×C31C2311yescharacteristic
87C4⋊C4×C31—21no—
88C4⋊C4×C31C2311yescharacteristic
89C22⋊C4×C31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92C22⋊Dic31D411yescharacteristic
93#92481—41no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4D411yescharacteristic
106C4×Dic31—21no—
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8—41no—
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C8×D31—41no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—42no—
115C23×C31—42no—
116C23×C31—81no—
117C23×C31C2×D411yescharacteristic
118C22×D31—21no—
119C22×D31—42no—
120C22×D31—42no—
121C22×D31—81no—
122C22×D31C2×D411yescharacteristic
123Q8×C31—21no—
124Q8×C31—21no—
125D4×C31—21no—
126D4×C31—21no—
127D4×C31—21no—
128D4×C31—42no—
129D4×C31#4112yes—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31C2×D411yescharacteristic
135C2×C4×C31C2411yescharacteristic
136C22⋊D31—42no—
137C22⋊D31—42no—
138C22⋊D31—42no—
139C22⋊D31—42no—
140C22⋊D31—81no—
141C22⋊D31SD1614yescomplemented
142C2×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—21no—
145C2×Dic31—42no—
146C2×Dic31—81no—
147C2×Dic31C2×D411yescharacteristic
148C2×Dic31C2×D411yescharacteristic
149C2×Dic31C2×D411yescharacteristic
150D124—21no—
151D124—21no—
152C4×D31—21no—
153C4×D31—21no—
154C4×D31—81no—
155Dic62—81no—
156C8×C31—21no—
157C8×C31—21no—
158C31⋊C8—21no—
159C31⋊C8—21no—
160#3295—311nomaximal, Sylow
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—22no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31—41no—
169C22×C31—84no—
170C22×C31C2×SD1612yes—
171C22×C31C22×D411yescharacteristic
172C2×D31—21no—
173C2×D31—21no—
174C2×D31—41no—
175C2×D31—41no—
176C2×D31—41no—
177C2×D31—84no—
178C2×D31C2×SD1612yes—
179C4×C31—21no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31C2×#4111yescharacteristic
183C4×C31H(5,𝔽2)11yescharacteristic
184Dic31—21no—
185Dic31—21no—
186Dic31—41no—
187Dic31—41no—
188Dic31—41no—
189Dic31C2×SD1612yes—
190#554—311no—
191D42—311no—
192#486—311no—
193#481—311no—
194#481—311no—
195#476—311no—
196#465—311no—
197#465—311no—
198#460—311no—
199#450—311no—
200#450D3111yescharacteristic, complemented
201C4×SD16—311no—
202C8×D4—311no—
203C2×#102—311no—
204C2×#102—311no—
205C2×C31—22no—
206C2×C31—42no—
207C2×C31—81no—
208C2×C31#54611yescharacteristic
209C2×C31C22×SD1611yescharacteristic
210C2×C31#57611yescharacteristic
211D31—22no—
212D31—81no—
213C22×D4—311no—
214C22×D4—621no—
215C22×D4C2×D3111yescharacteristic
216C2×SD16—311no—
217C2×SD16C2×D3111yescharacteristic
218C2×SD16C2×D3111yescharacteristic, complemented
219C22×C8—311no—
220C22×C8—311no—
221C4⋊Q8—311no—
222#127—311no—
223#125—621no—
224C22⋊Q8—311no—
225C22⋊Q8—621no—
226C22⋊Q8—621no—
227C22⋊Q8C2×D3111yescharacteristic, complemented
228#121—311no—
229#121—311no—
230#121—621no—
231#120—621no—
232#120—621no—
233C4×Q8—311no—
234C4×D4—311no—
235C4×D4—311no—
236C4×D4—621no—
237C2×C4⋊C4—311no—
238C2×C4⋊C4—311no—
239#106—311no—
240#106—311no—
241#106—311no—
242C4⋊C8—311no—
243#103—311no—
244#102—311no—
245#102—311no—
246#102—311no—
247#102—311no—
248#102—311no—
249#102—311no—
250#102—311no—
251#102C2×D3111yescharacteristic
252#102C2×D3111yescharacteristic, complemented
253C22⋊C8—311no—
254C22⋊C8C2×D3111yescharacteristic, complemented
255C4×C8—311no—
256C31#329511yescharacteristic, complemented, Sylow
257C24—21no—
258C24—621no—
259C2×Q8—621no—
260C2×Q8C22×D3111yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—311no—
265C2×D4—311no—
266C2×D4—621no—
267C2×D4—621no—
268C2×D4—621no—
269C2×D4—622no—
270C2×D4—621no—
271C2×D4—621no—
272C2×D4—1241no—
273C2×D4—1244no—
274C2×D4C22×D3111yescharacteristic
275C2×D4C22×D3111yescharacteristic
276C22×C4—311no—
277C22×C4—621no—
278C22×C4—621no—
279C22×C4—621no—
280C22×C4C22×D3111yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—1241no—
284C2×C8—311no—
285C2×C8—311no—
286C2×C8—1241no—
287C2×C8—1241no—
288C2×C8C22×D3111yescharacteristic
289C2×C8C22×D3111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—311no—
292C4⋊C4—311no—
293C4⋊C4—311no—
294C4⋊C4—311no—
295C4⋊C4—621no—
296C4⋊C4—621no—
297C4⋊C4—621no—
298C4⋊C4—621no—
299C4⋊C4—621no—
300C4⋊C4C22×D3111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—311no—
303C22⋊C4—311no—
304C22⋊C4—621no—
305C22⋊C4—621no—
306C22⋊C4—621no—
307C22⋊C4—621no—
308C42—311no—
309C42—621no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—311no—
316C23—621no—
317C23—1242no—
318C23—1242no—
319C23—2481no—
320C23D4×D3111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—2481no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—314no—
329D4—621no—
330D4—621no—
331D4—1242no—
332D4—1242no—
333D4—1242no—
334D4—1242no—
335D4—2481no—
336D4#9249712yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—311no—
342C2×C4—311no—
343C2×C4—311no—
344C2×C4—621no—
345C2×C4—621no—
346C2×C4—621no—
347C2×C4—621no—
348C2×C4—621no—
349C2×C4—1242no—
350C2×C4—2481no—
351C2×C4—2481no—
352C2×C4D4×D3111yescharacteristic
353C2×C4C23×D3111yescharacteristic
354C8—21no—
355C8—21no—
356C8—621no—
357C8—621no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—312no—
368C22—621no—
369C22—621no—
370C22—1241no—
371C22—1241no—
372C22—1241no—
373C22—2484no—
374C22SD16×D3112yes—
375C22C2×D4×D3111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—312no—
380C4—621no—
381C4—621no—
382C4—1241no—
383C4—1241no—
384C4—1241no—
385C4C2×#9249711yescharacteristic
386C4#1175856111yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—622no—
391C2—2481no—
392C2#1452168611yescharacteristic
393C2C2×SD16×D3111yescharacteristic
394C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#450C2
socleC22×C31C22×D4
prime radicalD4×C22⋊D31C2
hypercenter#450D31
hypocenterC31#3295
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14521757C2semidirect
3. #14521394C2semidirect
4. #14521368C2semidirect
5. #14521366C2semidirect
6. #14521337C2semidirect
7. #14521280C2semidirect
8. #14521275C2semidirect
9. #14521247C2semidirect
10. #14521198C2semidirect
11. SD16×Dic31C2semidirect
12. (C22⋊D31)⋊C8C2semidirect
13. C2×#11758420C2semidirect
14. #102×D31C2semidirect
15. C31×#450C2semidirect
20. C2×SD16×C31C22semidirect
21. C31×C22⋊Q8C22semidirect
23. #11758523C22semidirect
24. Q8×Dic31C22semidirect
25. C2×#92481C22semidirect
33. C2×C4⋊Dic31C22semidirect
34. C22×C31⋊C8C22semidirect
35. C2×C8×D31C22semidirect
37. C4⋊C4×D31C22semidirect
39. #11758465C22semidirect
43. C31×#102C22semidirect
44. C31×C22⋊C8C22semidirect
45. #11758423C22semidirect
48. #11758420C22semidirect
49. #11758420C22semidirect
50. #11758409C22semidirect
51. #11758409C22semidirect
52. (C2×D31)⋊C8C22semidirect
53. #11758405C22semidirect
54. #11758405C22semidirect
55. Dic31⋊C8C22semidirect
56. C8×Dic31C22semidirect
57. #11758397C22semidirect
58. #11758396C22semidirect
141. C22⋊D31SD16semidirect
200. #450D31semidirect
218. C2×SD16C2×D31semidirect
227. C22⋊Q8C2×D31semidirect
252. #102C2×D31semidirect
254. C22⋊C8C2×D31semidirect
256. C31#3295semidirect

Maximal subgroups

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

subgroupindex
#145217572
D4×C22⋊D312
#145213942
#145213682
#145213662
#145213372
#145212802
#145212752
#145212472
#145211982
SD16×Dic312
(C22⋊D31)⋊C82
C2×#117584202
#102×D312
C31×#4502
#329531