Finite Group Databasebeta

← #16857530

Subgroups — #16857530

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
2#14521683C211yesmaximal, characteristic
3#14521394C211yesmaximal, characteristic, complemented
4#14521369C211yesmaximal, characteristic, complemented
5#14521365C211yesmaximal, characteristic, complemented
6#14521338C211yesmaximal, characteristic, complemented
7#14521281C211yesmaximal, characteristic, complemented
8#14521247C211yesmaximal, characteristic, complemented
9#14521199C211yesmaximal, characteristic, complemented
10#14521198C211yesmaximal, characteristic, complemented
11#14521134C211yesmaximal, characteristic, complemented
12C8×C22⋊D31C211yesmaximal, characteristic, complemented
13C2×#11758409C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#465C211yesmaximal, characteristic, complemented
16C2×D4×D31—21no—
17C2×D4×D31C2211yescharacteristic
18C22×D124C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic, complemented
20C22×C8×C31C2211yescharacteristic, complemented
21C31×C22⋊Q8C2211yescharacteristic, complemented
22C31×#121C2211yescharacteristic
23#11758523C2211yescharacteristic, complemented
24Q8×Dic31C2211yescharacteristic, complemented
25C2×#92481C2211yescharacteristic
26C2×#92481C2211yescharacteristic, complemented
27#11758517C2211yescharacteristic
28#11758514—21no—
29C4×C22⋊D31C2211yescharacteristic
30C2×C4⋊Dic31C2211yescharacteristic, complemented
31C2×C8×D31C2211yescharacteristic, complemented
32#11758474—21no—
33#11758472C2211yescharacteristic
34#11758470C2211yescharacteristic
35C4⋊C4×D31C2211yescharacteristic, complemented
36#11758466—21no—
37#11758465C2211yescharacteristic, complemented
38#11758461—21no—
39#11758459—21no—
40(C22⋊D31)⋊C4—21no—
41#11758455—21no—
42C31×#106C2211yescharacteristic, complemented
43C31×#103C2211yescharacteristic, complemented
44C31×#102C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic, complemented
47C22⋊(C31⋊C8)C2211yescharacteristic, complemented
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic, complemented
51#11758409C2211yescharacteristic, complemented
52(C2×D31)⋊C8C2211yescharacteristic, complemented
53Dic31⋊C8C2211yescharacteristic, complemented
54C8×Dic31C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic, complemented
57#11758396C2211yescharacteristic, complemented
58#11758396C2211yescharacteristic, complemented
59C23×D31—21no—
60C23×D31—21no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31C2311yescharacteristic
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C2×C22⋊D31—21no—
68C2×C22⋊D31D411yescharacteristic
69C22×Dic31—21no—
70D4×D31—22no—
71D4×D31—41no—
72D4×D31—44no—
73C2×D124—22no—
74C2×D124—21no—
75C2×D124—21no—
76C2×D124—41no—
77C2×D124C2311yescharacteristic
78C2×D124C2311yescharacteristic
79C2×C4×D31—21no—
80C2×C4×D31—21no—
81C2×C4×D31C2311yescharacteristic
82C2×Dic62—21no—
83SD16×C31—41no—
84C2×C8×C31—41no—
85C2×C8×C31C2311yescharacteristic
86C2×C8×C31C2311yescharacteristic
87C4⋊C4×C31—21no—
88C4⋊C4×C31C2311yescharacteristic
89C4⋊C4×C31C2311yescharacteristic
90C22⋊C4×C31—21no—
91C22⋊C4×C31—21no—
92C22⋊Dic31D411yescharacteristic
93#92481—22no—
94#92481—41no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4D411yescharacteristic
99C4⋊Dic31—21no—
100C4⋊Dic31—21no—
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106Dic31⋊C4D411yescharacteristic
107C4×Dic31—21no—
108C4×Dic31C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C8×D31—41no—
112C23×C31—21no—
113C23×C31C2×D411yescharacteristic
114C22×D31—21no—
115C22×D31—21no—
116C22×D31—42no—
117C22×D31—42no—
118C22×D31—42no—
119C22×D31—42no—
120C22×D31—81no—
121C22×D31—81no—
122C22×D31C2×D411yescharacteristic
123Q8×C31—21no—
124Q8×C31—21no—
125D4×C31—21no—
126D4×C31—21no—
127D4×C31—42no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31C2×D411yescharacteristic
134C2×C4×C31C2411yescharacteristic
135C22⋊D31—42no—
136C22⋊D31—42no—
137C22⋊D31—81no—
138C22⋊D31SD1614yescomplemented
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—81no—
142C2×Dic31C2×D411yescharacteristic
143C2×Dic31C2×D411yescharacteristic
144C2×Dic31C2×D411yescharacteristic
145D124—21no—
146D124—21no—
147D124—21no—
148D124—42no—
149D124—42no—
150D124#4112yes—
151C4×D31—21no—
152C4×D31—21no—
153C4×D31—42no—
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—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31C2×SD1612yes—
167C22×C31C22×D411yescharacteristic
168C2×D31—21no—
169C2×D31—21no—
170C2×D31—22no—
171C2×D31—41no—
172C2×D31—41no—
173C2×D31—41no—
174C2×D31—41no—
175C2×D31—41no—
176C2×D31—84no—
177C2×D31—84no—
178C2×D31C2×SD1612yes—
179C4×C31—21no—
180C4×C31—41no—
181C4×C31—41no—
182C4×C31—41no—
183C4×C31C2×#4111yescharacteristic
184C4×C31H(5,𝔽2)11yescharacteristic
185Dic31—21no—
186Dic31—21no—
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#465D3111yescharacteristic, complemented
198#460—311no—
199#450—311no—
200#450—311no—
201C4×SD16—311no—
202C8×D4—311no—
203C2×#102—311no—
204C2×#102—311no—
205C2×C31—22no—
206C2×C31—81no—
207C2×C31#54611yescharacteristic
208C2×C31C22×SD1611yescharacteristic
209C2×C31#57611yescharacteristic
210D31—22no—
211D31—42no—
212D31—81no—
213C22×D4—311no—
214C22×D4—311no—
215C22×D4—621no—
216C2×SD16—311no—
217C2×SD16—311no—
218C2×SD16C2×D3111yescharacteristic, complemented
219C22×C8—311no—
220C22×C8C2×D3111yescharacteristic, complemented
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—621no—
230#121C2×D3111yescharacteristic
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#106C2×D3111yescharacteristic, complemented
242C4⋊C8—311no—
243#103C2×D3111yescharacteristic, complemented
244#102—311no—
245#102—311no—
246#102—311no—
247#102—311no—
248#102—311no—
249#102—311no—
250#102—311no—
251#102—311no—
252#102C2×D3111yescharacteristic, complemented
253C22⋊C8—311no—
254C22⋊C8—311no—
255C4×C8—311no—
256C31#329511yescharacteristic, complemented, Sylow
257C24—621no—
258C24—621no—
259C2×Q8—621no—
260C2×Q8C22×D3111yescharacteristic
261C2×D4—21no—
262C2×D4—311no—
263C2×D4—311no—
264C2×D4—311no—
265C2×D4—622no—
266C2×D4—621no—
267C2×D4—621no—
268C2×D4—621no—
269C2×D4—621no—
270C2×D4—622no—
271C2×D4—621no—
272C2×D4—1241no—
273C2×D4—1241no—
274C2×D4—1244no—
275C2×D4C22×D3111yescharacteristic
276C22×C4—311no—
277C22×C4—621no—
278C22×C4—621no—
279C22×C4—621no—
280C22×C4C22×D3111yescharacteristic
281SD16—41no—
282SD16—622no—
283SD16—1241no—
284C2×C8—41no—
285C2×C8—311no—
286C2×C8—311no—
287C2×C8—1241no—
288C2×C8C22×D3111yescharacteristic
289C2×C8C22×D3111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—311no—
292C4⋊C4—311no—
293C4⋊C4—311no—
294C4⋊C4—621no—
295C4⋊C4—621no—
296C4⋊C4—621no—
297C4⋊C4—621no—
298C4⋊C4—621no—
299C4⋊C4C22×D3111yescharacteristic
300C4⋊C4C22×D3111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—311no—
304C22⋊C4—311no—
305C22⋊C4—621no—
306C22⋊C4—621no—
307C22⋊C4—621no—
308C42—311no—
309C42—621no—
310C23—21no—
311C23—311no—
312C23—621no—
313C23—621no—
314C23—1242no—
315C23—1242no—
316C23—1242no—
317C23—1242no—
318C23—2481no—
319C23—2481no—
320C23D4×D3111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—2481no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—314no—
328D4—312no—
329D4—621no—
330D4—621no—
331D4—621no—
332D4—1242no—
333D4—1242no—
334D4—1242no—
335D4—1242no—
336D4—2481no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—311no—
343C2×C4—311no—
344C2×C4—311no—
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—41no—
361C22—41no—
362C22—41no—
363C22—312no—
364C22—621no—
365C22—621no—
366C22—622no—
367C22—1241no—
368C22—1241no—
369C22—1241no—
370C22—1241no—
371C22—1241no—
372C22—2484no—
373C22—2484no—
374C22SD16×D3112yes—
375C22C2×D4×D3111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—312no—
381C4—621no—
382C4—621no—
383C4—1241no—
384C4—1241no—
385C4#1175856111yescharacteristic
386C4#41×D3111yescharacteristic
387C2—22no—
388C2—81no—
389C2—622no—
390C2—1242no—
391C2—2481no—
392C2#1452168811yescharacteristic
393C2C2×SD16×D3111yescharacteristic
394C2#1452185111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#465C2
socleC22×C31C22×D4
prime radical#14521683C2
hypercenter#465D31
hypocenterC31#3295
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14521757C2semidirect
3. #14521394C2semidirect
4. #14521369C2semidirect
5. #14521365C2semidirect
6. #14521338C2semidirect
7. #14521281C2semidirect
8. #14521247C2semidirect
9. #14521199C2semidirect
10. #14521198C2semidirect
11. #14521134C2semidirect
12. C8×C22⋊D31C2semidirect
13. C2×#11758409C2semidirect
14. #102×D31C2semidirect
15. C31×#465C2semidirect
19. C2×SD16×C31C22semidirect
20. C22×C8×C31C22semidirect
21. C31×C22⋊Q8C22semidirect
23. #11758523C22semidirect
24. Q8×Dic31C22semidirect
26. C2×#92481C22semidirect
30. C2×C4⋊Dic31C22semidirect
31. C2×C8×D31C22semidirect
35. C4⋊C4×D31C22semidirect
37. #11758465C22semidirect
42. C31×#106C22semidirect
43. C31×#103C22semidirect
44. C31×#102C22semidirect
45. #11758420C22semidirect
46. #11758420C22semidirect
47. C22⋊(C31⋊C8)C22semidirect
50. #11758409C22semidirect
51. #11758409C22semidirect
52. (C2×D31)⋊C8C22semidirect
53. Dic31⋊C8C22semidirect
54. C8×Dic31C22semidirect
56. #11758397C22semidirect
57. #11758396C22semidirect
58. #11758396C22semidirect
138. C22⋊D31SD16semidirect
197. #465D31semidirect
218. C2×SD16C2×D31semidirect
220. C22×C8C2×D31semidirect
227. C22⋊Q8C2×D31semidirect
241. #106C2×D31semidirect
243. #103C2×D31semidirect
252. #102C2×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
#145216832
#145213942
#145213692
#145213652
#145213382
#145212812
#145212472
#145211992
#145211982
#145211342
C8×C22⋊D312
C2×#117584092
#102×D312
C31×#4652
#329531