Finite Group Databasebeta

← #16855901

Subgroups — #16855901

Order 3968.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521671C211yesmaximal, characteristic, complemented
2#14521521C211yesmaximal, characteristic, complemented
3#14521389C211yesmaximal, characteristic, complemented
4#14521375C211yesmaximal, characteristic, complemented
5#14521338C211yesmaximal, characteristic, complemented
6#14521327C211yesmaximal, characteristic, complemented
7#14521267C211yesmaximal, characteristic, complemented
8#14521266C211yesmaximal, characteristic, complemented
9#14521198C211yesmaximal, characteristic, complemented
10#14521184C211yesmaximal, characteristic
11#14521159C211yesmaximal, characteristic, complemented
12#14521147C211yesmaximal, characteristic, complemented
13C4×D248C211yesmaximal, characteristic, complemented
14#14521108C211yesmaximal, characteristic, complemented
15C4×SD16×C31C211yesmaximal, characteristic, complemented
16C2×D4×D31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C4×Q8×C31C2211yescharacteristic, complemented
19C4×D4×C31C2211yescharacteristic
20#11758524C2211yescharacteristic, complemented
21#11758523C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23D4×Dic31C2211yescharacteristic
24C2×#92479C2211yescharacteristic
25C4×C22⋊D31—21no—
26C2×(C2×D31)⋊C4—21no—
27C2×D248C2211yescharacteristic
28#11758473—21no—
29#11758472C2211yescharacteristic
30#11758471—21no—
31#11758470C2211yescharacteristic
32#11758469C2211yescharacteristic
33#11758465C2211yescharacteristic, complemented
34(C22⋊D31)⋊C4—21no—
35C22⋊C4×D31—21no—
36#11758453—21no—
37#11758452—21no—
38C4×D124C2211yescharacteristic
39C4×D124C2211yescharacteristic, complemented
40#11758449C2211yescharacteristic
41C31×#106C2211yescharacteristic, complemented
42C31×#103C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic
44C4×C8×C31C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic, complemented
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758406C2211yescharacteristic, complemented
52Dic31⋊C8C2211yescharacteristic, complemented
53Dic31⋊C8C2211yescharacteristic, complemented
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic, complemented
56#11758396C2211yescharacteristic, 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×D124—21no—
68C2×D124C2311yescharacteristic
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31C2311yescharacteristic
74C2×Dic62—21no—
75SD16×C31—22no—
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C4⋊C4×C31—21no—
79C4⋊C4×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C22⋊C4×C31—21no—
82C42×C31—21no—
83C42×C31C2311yescharacteristic
84C22⋊Dic31—21no—
85#92481—22no—
86#92479—22no—
87(C2×D31)⋊C4—21no—
88(C2×D31)⋊C4—21no—
89(C2×D31)⋊C4—21no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4D411yescharacteristic
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4D411yescharacteristic
102Dic31⋊C4D411yescharacteristic
103C4×Dic31—21no—
104C4×Dic31C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107D248—22no—
108C23×C31—21no—
109C22×D31—21no—
110C22×D31—24no—
111C22×D31—21no—
112C22×D31—81no—
113C22×D31—81no—
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—81no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2411yescharacteristic
126C22⋊D31—24no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—81no—
130C2×Dic31C2×D411yescharacteristic
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133D124—21no—
134D124—21no—
135D124—21no—
136D124—81no—
137D124#4112yes—
138C4×D31—21no—
139C4×D31—21no—
140C4×D31—81no—
141C4×D31—81no—
142C4×D31—81no—
143Dic62—81no—
144C8×C31—21no—
145C8×C31—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3118—311nomaximal, Sylow
149C22×C31—22no—
150C22×C31—41no—
151C22×C31—41no—
152C22×C31C22×D411yescharacteristic
153C2×D31—21no—
154C2×D31—22no—
155C2×D31—21no—
156C2×D31—21no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—84no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31C2×#4111yescharacteristic
169C4×C31C2×#4111yescharacteristic
170Dic31—21no—
171Dic31—21no—
172Dic31—21no—
173Dic31—41no—
174Dic31—41no—
175#542—311no—
176#518—311no—
177#485—311no—
178#482—311no—
179#476—311no—
180#474—311no—
181#463—311no—
182#463—311no—
183#450—311no—
184#447—311no—
185#442—311no—
186#440—311no—
187C4×SD16D3111yescharacteristic, complemented
188C4×D8—311no—
189#433—311no—
190C2×C31—42no—
191C2×C31#52511yescharacteristic
192C2×C31#57611yescharacteristic
193C2×C31#57711yescharacteristic
194D31—41no—
195D31—42no—
196D31—81no—
197C22×D4—311no—
198C2×SD16—311no—
199C2×SD16C2×D3111yescharacteristic
200C2×D8—311no—
201C2×D8—311no—
202C4⋊Q8—311no—
203#126—621no—
204#124—311no—
205#124—621no—
206#123—621no—
207C22⋊Q8—311no—
208C22⋊Q8—621no—
209#121—311no—
210C4×Q8C2×D3111yescharacteristic, complemented
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—621no—
216C4×D4—621no—
217C4×D4C2×D3111yescharacteristic
218#117—311no—
219#117—311no—
220C2×C22⋊C4—621no—
221C2×C22⋊C4—621no—
222#107—311no—
223#107—311no—
224#106—311no—
225#106C2×D3111yescharacteristic, complemented
226C4⋊C8—311no—
227C4⋊C8—311no—
228#103—311no—
229#103C2×D3111yescharacteristic, complemented
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102—311no—
235#102C2×D3111yescharacteristic
236C22⋊C8—311no—
237C22⋊C8—311no—
238#97—311no—
239C4×C8C2×D3111yescharacteristic, complemented
240C31#311811yescharacteristic, complemented, Sylow
241C24—621no—
242C2×Q8—621no—
243C2×Q8C22×D3111yescharacteristic
244C2×D4—311no—
245C2×D4—311no—
246C2×D4—621no—
247C2×D4—621no—
248C2×D4—622no—
249C2×D4—622no—
250C2×D4C22×D3111yescharacteristic
251C22×C4—21no—
252C22×C4—311no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257SD16—22no—
258SD16—622no—
259D8—622no—
260D8—622no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8C22×D3111yescharacteristic
264C2×C8C22×D3111yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—311no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4C22×D3111yescharacteristic
273C4⋊C4C22×D3111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—311no—
276C22⋊C4—311no—
277C22⋊C4—621no—
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—311no—
288C42—621no—
289C42C22×D3111yescharacteristic
290C23—21no—
291C23—311no—
292C23—624no—
293C23—621no—
294C23—621no—
295C23—2481no—
296C23—2481no—
297Q8—21no—
298Q8—21no—
299Q8—2481no—
300D4—21no—
301D4—312no—
302D4—624no—
303D4—621no—
304D4—621no—
305D4—621no—
306D4—2481no—
307D4#9249512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—311no—
313C2×C4—311no—
314C2×C4—311no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4—2481no—
323C2×C4D4×D3111yescharacteristic
324C2×C4D4×D3111yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—21no—
327C8—21no—
328C8—621no—
329C8—621no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—621no—
334C22—622no—
335C22—621no—
336C22—621no—
337C22—1241no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22—1241no—
342C22—2484no—
343C22C2×D4×D3111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—621no—
350C4—621no—
351C4—621no—
352C4—1241no—
353C4—1241no—
354C4C2×#9249511yescharacteristic
355C4#41×D3111yescharacteristic
356C2—42no—
357C2—1241no—
358C2—1242no—
359C2—2481no—
360C2#1452155811yescharacteristic
361C2#1452185111yescharacteristic
362C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×SD16×C31C2
socleC22×C31C22×D4
prime radical#14521184C2
hypercenterC4×SD16D31
hypocenterC31#3118
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #14521671C2semidirect
2. #14521521C2semidirect
3. #14521389C2semidirect
4. #14521375C2semidirect
5. #14521338C2semidirect
6. #14521327C2semidirect
7. #14521267C2semidirect
8. #14521266C2semidirect
9. #14521198C2semidirect
11. #14521159C2semidirect
12. #14521147C2semidirect
13. C4×D248C2semidirect
14. #14521108C2semidirect
15. C4×SD16×C31C2semidirect
18. C4×Q8×C31C22semidirect
20. #11758524C22semidirect
33. #11758465C22semidirect
39. C4×D124C22semidirect
41. C31×#106C22semidirect
42. C31×#103C22semidirect
44. C4×C8×C31C22semidirect
45. #11758423C22semidirect
48. #11758409C22semidirect
51. #11758406C22semidirect
52. Dic31⋊C8C22semidirect
53. Dic31⋊C8C22semidirect
55. #11758397C22semidirect
56. #11758396C22semidirect
57. #11758395C22semidirect
58. #11758391C22semidirect
187. C4×SD16D31semidirect
210. C4×Q8C2×D31semidirect
225. #106C2×D31semidirect
229. #103C2×D31semidirect
239. C4×C8C2×D31semidirect
240. C31#3118semidirect

Maximal subgroups

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

subgroupindex
#145216712
#145215212
#145213892
#145213752
#145213382
#145213272
#145212672
#145212662
#145211982
#145211842
#145211592
#145211472
C4×D2482
#145211082
C4×SD16×C312
#311831