Finite Group Databasebeta

← #16855808

Subgroups — #16855808

Order 3968.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521603C211yesmaximal, characteristic, complemented
2C4×D4×D31C211yesmaximal, characteristic
3#14521386C211yesmaximal, characteristic, complemented
4#14521383C211yesmaximal, characteristic, complemented
5#14521328C211yesmaximal, characteristic, complemented
6#14521327C211yesmaximal, characteristic, complemented
7#14521253C211yesmaximal, characteristic, complemented
8#14521252C211yesmaximal, characteristic, complemented
9#14521201C211yesmaximal, characteristic
10#14521198C211yesmaximal, characteristic
11#14521151C211yesmaximal, characteristic, complemented
12#14521149C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14#14521104C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×D4×D31C2211yescharacteristic
17C22×C4×D31—21no—
18C2×SD16×C31C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic, complemented
20C4×D4×C31C2211yescharacteristic
21#11758523C2211yescharacteristic
22#11758521C2211yescharacteristic, complemented
23C2×#92481C2211yescharacteristic
24D4×Dic31C2211yescharacteristic
25C2×#92480C2211yescharacteristic
26C4×C22⋊D31—21no—
27C2×#92470C2211yescharacteristic
28#11758474C2211yescharacteristic
29#11758473—21no—
30#11758470C2211yescharacteristic
31C4⋊C4×D31C2211yescharacteristic
32#11758466—21no—
33#11758465C2211yescharacteristic, complemented
34(C22⋊D31)⋊C4—21no—
35C22⋊C4×D31—21no—
36C4×D124C2211yescharacteristic
37#11758449—21no—
38C42×D31C2211yescharacteristic
39C4×Dic62—21no—
40C4×Dic62C2211yescharacteristic, complemented
41C31×#107C2211yescharacteristic, complemented
42C31×#103C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic
44C31×#97C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48(C2×D31)⋊C8C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50#11758406C2211yescharacteristic, complemented
51#11758404C2211yescharacteristic, complemented
52Dic31⋊C8C2211yescharacteristic, complemented
53Dic31⋊C8C2211yescharacteristic, complemented
54#11758398C2211yescharacteristic, complemented
55#11758397C2211yescharacteristic
56#11758395C2211yescharacteristic, complemented
57#11758395C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C22×Dic31—21no—
65D4×D31—22no—
66D4×D31—22no—
67C2×D124C2311yescharacteristic
68C2×C4×D31—21no—
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31—44no—
72C2×C4×D31D411yescharacteristic
73C2×C4×D31D411yescharacteristic
74C2×C4×D31C2311yescharacteristic
75C2×Dic62—21no—
76C2×Dic62C2311yescharacteristic
77SD16×C31—22no—
78C2×C8×C31C2311yescharacteristic
79C2×C8×C31C2311yescharacteristic
80C4⋊C4×C31—21no—
81C4⋊C4×C31C2311yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C42×C31—21no—
85C42×C31C2311yescharacteristic
86C22⋊Dic31—21no—
87#92481—22no—
88#92480—22no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93C4⋊Dic31—21no—
94C4⋊Dic31C2311yescharacteristic
95C4⋊Dic31C2311yescharacteristic
96Dic31⋊C4—21no—
97Dic31⋊C4—21no—
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31D411yescharacteristic
104C4×Dic31D411yescharacteristic
105C4×Dic31C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108#92470—22no—
109C23×C31—21no—
110C22×D31—24no—
111C22×D31—21no—
112C22×D31—42no—
113C22×D31—42no—
114C22×D31C2×D411yescharacteristic
115Q8×C31—21no—
116Q8×C31—21no—
117D4×C31—21no—
118D4×C31#4112yes—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—42no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C22⋊D31—24no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—42no—
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134D124—21no—
135D124#4112yes—
136C4×D31—22no—
137C4×D31—21no—
138C4×D31—21no—
139C4×D31—22no—
140C4×D31—42no—
141C4×D31—42no—
142C4×D31—42no—
143Dic62—21no—
144Dic62—21no—
145Dic62—42no—
146C8×C31—21no—
147C8×C31—21no—
148C31⋊C8—21no—
149C31⋊C8—21no—
150#3110—311nomaximal, Sylow
151C22×C31—22no—
152C22×C31—41no—
153C22×C31—41no—
154C22×C31C22×D411yescharacteristic
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—22no—
158C2×D31—48no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31#13712yes—
162C4×C31—21no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31C2×#4111yescharacteristic
168C4×C31C2×#4111yescharacteristic
169Dic31—21no—
170Dic31—21no—
171Dic31—41no—
172Dic31—41no—
173Dic31—41no—
174Dic31AGL(1,ℤ/8)12yes—
175#533—311no—
176C2×C4×D4—311no—
177#484—311no—
178#484—311no—
179#474—311no—
180#474—311no—
181#461—311no—
182#461—311no—
183#450—311no—
184#450—311no—
185#440—311no—
186#440—311no—
187#440—311no—
188#440D3111yescharacteristic, complemented
189#432—311no—
190C2×C31—42no—
191C2×C31#52511yescharacteristic
192C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C31C2×#13711yescharacteristic
194D31—22no—
195D31—42no—
196C22×D4—311no—
197C23×C4—621no—
198C2×SD16—311no—
199C2×SD16—311no—
200C2×SD16—311no—
201C2×SD16C2×D3111yescharacteristic
202C4⋊Q8—311no—
203C4⋊Q8—311no—
204#125—621no—
205C22⋊Q8—311no—
206C22⋊Q8—311no—
207C22⋊Q8—621no—
208C4×Q8—311no—
209C4×Q8—621no—
210C4×Q8C2×D3111yescharacteristic, complemented
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—621no—
215C4×D4—621no—
216C4×D4C2×D3111yescharacteristic
217#117—621no—
218C2×C4⋊C4—311no—
219C2×C22⋊C4—621no—
220C2×C42—311no—
221#107—311no—
222#107—311no—
223#107—311no—
224#107C2×D3111yescharacteristic, complemented
225C4⋊C8—311no—
226C4⋊C8—311no—
227#103—311no—
228#103—311no—
229#103—311no—
230#103C2×D3111yescharacteristic, complemented
231#102—311no—
232#102—311no—
233#102—311no—
234#102C2×D3111yescharacteristic
235C22⋊C8—311no—
236C22⋊C8—311no—
237#97—311no—
238#97C2×D3111yescharacteristic, complemented
239C31#311011yescharacteristic, complemented, Sylow
240C24—621no—
241C2×Q8—311no—
242C2×Q8—621no—
243C2×Q8C22×D3111yescharacteristic
244C2×D4—311no—
245C2×D4—621no—
246C2×D4—622no—
247C2×D4—622no—
248C2×D4C22×D3111yescharacteristic
249C22×C4—21no—
250C22×C4—311no—
251C22×C4—311no—
252C22×C4—311no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—1244no—
258SD16—22no—
259SD16—622no—
260SD16—622no—
261SD16—622no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8C22×D3111yescharacteristic
265C2×C8C22×D3111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4—621no—
274C4⋊C4—621no—
275C4⋊C4—621no—
276C4⋊C4C22×D3111yescharacteristic
277C4⋊C4C22×D3111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C42—21no—
285C42—311no—
286C42—311no—
287C42—311no—
288C42—621no—
289C42C22×D3111yescharacteristic
290C23—21no—
291C23—311no—
292C23—624no—
293C23—621no—
294C23—1242no—
295C23—1242no—
296Q8—21no—
297Q8—21no—
298Q8—621no—
299Q8—621no—
300Q8—1242no—
301D4—21no—
302D4—312no—
303D4—624no—
304D4—621no—
305D4#9249512yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—311no—
311C2×C4—311no—
312C2×C4—311no—
313C2×C4—622no—
314C2×C4—622no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—1242no—
321C2×C4—1242no—
322C2×C4—1242no—
323C2×C4—1242no—
324C2×C4D4×D3111yescharacteristic
325C2×C4D4×D3111yescharacteristic
326C2×C4C23×D3111yescharacteristic
327C8—21no—
328C8—21no—
329C8—621no—
330C8—621no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—312no—
335C22—621no—
336C22—621no—
337C22—622no—
338C22—1248no—
339C22—1241no—
340C22—1241no—
341C22C2×D4×D3111yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—312no—
348C4—621no—
349C4—621no—
350C4—1241no—
351C4—1241no—
352C4—1241no—
353C4C2×#9249511yescharacteristic
354C4#41×D3111yescharacteristic
355C2—42no—
356C2—622no—
357C2—1242no—
358C2#1452155811yescharacteristic
359C2AGL(1,ℤ/8)×D3111yescharacteristic
360C2#137×D3111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
prime radicalC2×D4×D31C22
hypercenter#440D31
hypocenterC31#3110
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14521603C2semidirect
3. #14521386C2semidirect
4. #14521383C2semidirect
5. #14521328C2semidirect
6. #14521327C2semidirect
7. #14521253C2semidirect
8. #14521252C2semidirect
11. #14521151C2semidirect
12. #14521149C2semidirect
13. #14521147C2semidirect
14. #14521104C2semidirect
15. C31×#440C2semidirect
19. C4×Q8×C31C22semidirect
22. #11758521C22semidirect
33. #11758465C22semidirect
40. C4×Dic62C22semidirect
41. C31×#107C22semidirect
42. C31×#103C22semidirect
44. C31×#97C22semidirect
45. #11758423C22semidirect
50. #11758406C22semidirect
51. #11758404C22semidirect
52. Dic31⋊C8C22semidirect
53. Dic31⋊C8C22semidirect
54. #11758398C22semidirect
56. #11758395C22semidirect
57. #11758395C22semidirect
58. #11758391C22semidirect
188. #440D31semidirect
210. C4×Q8C2×D31semidirect
224. #107C2×D31semidirect
230. #103C2×D31semidirect
238. #97C2×D31semidirect
239. C31#3110semidirect

Maximal subgroups

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

subgroupindex
#145216032
C4×D4×D312
#145213862
#145213832
#145213282
#145213272
#145212532
#145212522
#145212012
#145211982
#145211512
#145211492
#145211472
#145211042
C31×#4402
#311031