Finite Group Databasebeta

← #16857665

Subgroups — #16857665

Order 3968.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521699C211yesmaximal, characteristic, complemented
2#14521687C211yesmaximal, characteristic, complemented
3#14521410C211yesmaximal, characteristic, complemented
4#14521378C211yesmaximal, characteristic, complemented
5#14521368C211yesmaximal, characteristic, complemented
6#14521337C211yesmaximal, characteristic, complemented
7#14521300C211yesmaximal, characteristic, complemented
8#14521275C211yesmaximal, characteristic, complemented
9#14521266C211yesmaximal, characteristic, complemented
10#14521181C211yesmaximal, characteristic, complemented
11#14521161C211yesmaximal, characteristic, complemented
12#14521123C211yesmaximal, characteristic, complemented
13#14521050C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#449C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×#92497—21no—
18C2×D4×D31C2211yescharacteristic
19C2×SD16×C31C2211yescharacteristic, complemented
20C2×D8×C31C2211yescharacteristic
21C31×#121C2211yescharacteristic, complemented
22#11758524C2211yescharacteristic
23#11758523C2211yescharacteristic
24#11758516—21no—
25#11758515C2211yescharacteristic
26#11758514—21no—
27#11758512—21no—
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic, complemented
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758506—21no—
33C4×C22⋊D31C2211yescharacteristic
34C2×(C2×D31)⋊C4—21no—
35C2×C4⋊Dic31C2211yescharacteristic, complemented
36C2×#92474C2211yescharacteristic, complemented
37C2×C8×D31C2211yescharacteristic
38C4⋊C4×D31C2211yescharacteristic
39#11758465C2211yescharacteristic, complemented
40#11758460—21no—
41#11758455—21no—
42C31×#103C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758423C2211yescharacteristic, complemented
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic, complemented
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52(C2×D31)⋊C8C2211yescharacteristic
53#11758405C2211yescharacteristic, complemented
54#11758405C2211yescharacteristic, complemented
55#11758403C2211yescharacteristic, complemented
56Dic31⋊C8C2211yescharacteristic, complemented
57#11758397C2211yescharacteristic
58#11758396C2211yescharacteristic, complemented
59C23×D31—21no—
60#41×C31—22no—
61#41×C31—41no—
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31—21no—
64C2×D4×C31—21no—
65C2×D4×C31C2311yescharacteristic
66C2×D4×C31C2311yescharacteristic
67C22×C4×C31—21no—
68C22×C4×C31C2311yescharacteristic
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31D411yescharacteristic
73C22×Dic31—21no—
74C22×Dic31—21no—
75C22×Dic31—21no—
76#92497—44no—
77D4×D31—22no—
78D4×D31—41no—
79C2×D124C2311yescharacteristic
80C2×C4×D31—21no—
81C2×C4×D31C2311yescharacteristic
82C2×Dic62—21no—
83SD16×C31—41no—
84D8×C31—22no—
85C2×C8×C31C2311yescharacteristic
86C2×C8×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C22⋊C4×C31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92C22⋊Dic31D411yescharacteristic
93#92479—41no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4D411yescharacteristic
99C4⋊Dic31—21no—
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106Dic31⋊C4D411yescharacteristic
107C4×Dic31C2311yescharacteristic
108#92474—41no—
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C8×D31—41no—
112C23×C31—21no—
113C23×C31—21no—
114C23×C31C2×D411yescharacteristic
115C22×D31—21no—
116C22×D31—42no—
117C22×D31—42no—
118C22×D31—81no—
119C22×D31C2×D411yescharacteristic
120Q8×C31—21no—
121Q8×C31—21no—
122D4×C31—21no—
123D4×C31—21no—
124D4×C31—21no—
125D4×C31—42no—
126D4×C31—42no—
127D4×C31#4112yescomplemented
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—42no—
133C2×C4×C31C2×D411yescharacteristic
134C2×C4×C31C2411yescharacteristic
135C22⋊D31—22no—
136C22⋊D31—42no—
137C22⋊D31—42no—
138C22⋊D31—81no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—21no—
142C2×Dic31—42no—
143C2×Dic31—42no—
144C2×Dic31—81no—
145C2×Dic31C2×D411yescharacteristic
146C2×Dic31C2×D411yescharacteristic
147C2×Dic31C2×D411yescharacteristic
148D124—21no—
149D124—21no—
150C4×D31—21no—
151C4×D31—21no—
152C4×D31—42no—
153Dic62—42no—
154C8×C31—21no—
155C8×C31—21no—
156C31⋊C8—21no—
157C31⋊C8—21no—
158#3306—311nomaximal, Sylow
159C22×C31—22no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—21no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31C22×D411yescharacteristic
169C2×D31—21no—
170C2×D31—21no—
171C2×D31—41no—
172C2×D31—41no—
173C2×D31—41no—
174C2×D31—84no—
175C2×D31AGL(1,ℤ/8)12yes—
176C4×C31—21no—
177C4×C31—41no—
178C4×C31—41no—
179C4×C31C2×#4111yescharacteristic
180C4×C31H(5,𝔽2)11yescharacteristic
181Dic31—21no—
182Dic31—21no—
183Dic31—21no—
184Dic31—41no—
185Dic31—41no—
186Dic31—41no—
187#547—311no—
188#546—311no—
189#489—311no—
190#483—311no—
191#481—311no—
192#476—311no—
193#469—311no—
194#465—311no—
195#463—311no—
196#449D3111yescharacteristic, complemented
197#447—311no—
198#442—311no—
199#435—311no—
200#417—311no—
201C2×#102—311no—
202C2×C31—42no—
203C2×C31—41no—
204C2×C31—81no—
205C2×C31#54611yescharacteristic
206C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C31#57711yescharacteristic
208D31—22no—
209D31—81no—
210C2×#41—621no—
211C2×#41C2×D3111yescharacteristic
212C22×D4—311no—
213C2×SD16C2×D3111yescharacteristic, complemented
214C2×D8—311no—
215C2×D8C2×D3111yescharacteristic
216C2×M16—311no—
217C22×C8—311no—
218C4⋊Q8—311no—
219#124—311no—
220#123—621no—
221#123—621no—
222#123—621no—
223C22⋊Q8—311no—
224C22⋊Q8—621no—
225#121—311no—
226#121—311no—
227#121—621no—
228#121C2×D3111yescharacteristic, complemented
229#120—621no—
230C4×D4—311no—
231C4×D4—311no—
232C4×D4—311no—
233C2×C4⋊C4—311no—
234C2×C4⋊C4—311no—
235C2×C22⋊C4—621no—
236#106—311no—
237#106—311no—
238#106—311no—
239C4⋊C8—311no—
240#103—311no—
241#103—311no—
242#103C2×D3111yescharacteristic, complemented
243#102—311no—
244#102—311no—
245#102—311no—
246#102—311no—
247#102—311no—
248#102—311no—
249#102C2×D3111yescharacteristic
250C22⋊C8—311no—
251C22⋊C8C2×D3111yescharacteristic, complemented
252#97—311no—
253C31#330611yescharacteristic, complemented, Sylow
254C24—621no—
255#41—22no—
256#41—41no—
257#41—1244no—
258C2×Q8—621no—
259C2×Q8C22×D3111yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—311no—
263C2×D4—311no—
264C2×D4—621no—
265C2×D4—622no—
266C2×D4—621no—
267C2×D4—621no—
268C2×D4—1241no—
269C2×D4C22×D3111yescharacteristic
270C2×D4C22×D3111yescharacteristic
271C22×C4—21no—
272C22×C4—311no—
273C22×C4—621no—
274C22×C4—621no—
275C22×C4—621no—
276C22×C4—621no—
277C22×C4C22×D3111yescharacteristic
278SD16—41no—
279D8—22no—
280D8—1241no—
281M16—1241no—
282C2×C8—311no—
283C2×C8—311no—
284C2×C8—1241no—
285C2×C8C22×D3111yescharacteristic
286C2×C8C22×D3111yescharacteristic
287C4⋊C4—311no—
288C4⋊C4—311no—
289C4⋊C4—311no—
290C4⋊C4—311no—
291C4⋊C4—621no—
292C4⋊C4—621no—
293C4⋊C4—621no—
294C4⋊C4—621no—
295C4⋊C4C22×D3111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—311no—
298C22⋊C4—311no—
299C22⋊C4—621no—
300C22⋊C4—621no—
301C22⋊C4—621no—
302C22⋊C4—621no—
303C22⋊C4—621no—
304C22⋊C4—621no—
305C22⋊C4—621no—
306C42—311no—
307C23—21no—
308C23—21no—
309C23—311no—
310C23—621no—
311C23—1242no—
312C23—1242no—
313C23—2481no—
314C23D4×D3111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1242no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—622no—
324D4—621no—
325D4—621no—
326D4—1242no—
327D4—1242no—
328D4—2481no—
329D4#9249712yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—311no—
336C2×C4—311no—
337C2×C4—311no—
338C2×C4—621no—
339C2×C4—621no—
340C2×C4—621no—
341C2×C4—621no—
342C2×C4—621no—
343C2×C4—1242no—
344C2×C4—1242no—
345C2×C4—1242no—
346C2×C4—2481no—
347C2×C4D4×D3111yescharacteristic
348C2×C4C23×D3111yescharacteristic
349C8—21no—
350C8—21no—
351C8—621no—
352C8—621no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—312no—
363C22—621no—
364C22—621no—
365C22—1241no—
366C22—1241no—
367C22—1241no—
368C22—2484no—
369C22C2×D4×D3111yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—621no—
374C4—621no—
375C4—621no—
376C4—1241no—
377C4—1241no—
378C4—1241no—
379C4C2×#9249711yescharacteristic
380C4#1175856111yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—622no—
385C2—2481no—
386C2#1452168611yescharacteristic
387C2AGL(1,ℤ/8)×D3111yescharacteristic
388C2#1452185611yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#449C2
socleC22×C31C22×D4
hypercenter#449D31
hypocenterC31#3306
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14521699C2semidirect
2. #14521687C2semidirect
3. #14521410C2semidirect
4. #14521378C2semidirect
5. #14521368C2semidirect
6. #14521337C2semidirect
7. #14521300C2semidirect
8. #14521275C2semidirect
9. #14521266C2semidirect
10. #14521181C2semidirect
11. #14521161C2semidirect
12. #14521123C2semidirect
13. #14521050C2semidirect
14. #102×D31C2semidirect
15. C31×#449C2semidirect
19. C2×SD16×C31C22semidirect
21. C31×#121C22semidirect
29. D4×Dic31C22semidirect
35. C2×C4⋊Dic31C22semidirect
36. C2×#92474C22semidirect
39. #11758465C22semidirect
42. C31×#103C22semidirect
44. C31×C22⋊C8C22semidirect
45. #11758423C22semidirect
46. #11758423C22semidirect
49. #11758420C22semidirect
53. #11758405C22semidirect
54. #11758405C22semidirect
55. #11758403C22semidirect
56. Dic31⋊C8C22semidirect
58. #11758396C22semidirect
127. D4×C31#41semidirect
196. #449D31semidirect
213. C2×SD16C2×D31semidirect
228. #121C2×D31semidirect
242. #103C2×D31semidirect
251. C22⋊C8C2×D31semidirect
253. C31#3306semidirect
329. D4#92497semidirect

Maximal subgroups

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

subgroupindex
#145216992
#145216872
#145214102
#145213782
#145213682
#145213372
#145213002
#145212752
#145212662
#145211812
#145211612
#145211232
#145210502
#102×D312
C31×#4492
#330631