Finite Group Databasebeta

← #16855895

Subgroups — #16855895

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#14521670C211yesmaximal, characteristic, complemented
2#14521390C211yesmaximal, characteristic, complemented
3#14521373C211yesmaximal, characteristic, complemented
4#14521339C211yesmaximal, characteristic, complemented
5#14521329C211yesmaximal, characteristic, complemented
6#14521264C211yesmaximal, characteristic, complemented
7#14521264C211yesmaximal, characteristic, complemented
8#14521200C211yesmaximal, characteristic, complemented
9#14521183C211yesmaximal, characteristic
10#14521159C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12C4×#92480C211yesmaximal, characteristic, complemented
13C4×#92479C211yesmaximal, characteristic, complemented
14#14521110C211yesmaximal, characteristic, complemented
15C31×#518C211yesmaximal, characteristic, complemented
16C22×D4×C31C2211yescharacteristic
17C4×D4×C31—21no—
18C4×D4×C31—21no—
19C4×D4×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21C4×D4×C31C2211yescharacteristic
22C4×D4×C31C2211yescharacteristic
23C31×#117C2211yescharacteristic
24C31×#117C2211yescharacteristic
25C2×C22⋊C4×C31—21no—
26C2×C22⋊C4×C31—21no—
27C2×#92480C2211yescharacteristic
28C2×#92480C2211yescharacteristic
29C2×#92479C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758501C2211yescharacteristic
33#11758475—21no—
34#11758473—21no—
35#11758462—21no—
36#11758460—21no—
37#11758452C2211yescharacteristic, complemented
38C4×D124C2211yescharacteristic, complemented
39#11758446C2211yescharacteristic, complemented
40C4×Dic62C2211yescharacteristic, complemented
41#11758420C2211yescharacteristic
42#11758420C2211yescharacteristic
43#11758420C2211yescharacteristic
44#11758420C2211yescharacteristic
45C22⋊(C31⋊C8)C2211yescharacteristic
46C22⋊(C31⋊C8)C2211yescharacteristic
47#11758398C2211yescharacteristic, complemented
48#11758398C2211yescharacteristic, complemented
49#11758397C2211yescharacteristic, complemented
50#11758397C2211yescharacteristic, complemented
51#11758396C2211yescharacteristic, complemented
52#11758396C2211yescharacteristic, complemented
53#11758395C2211yescharacteristic, complemented
54#11758395C2211yescharacteristic, complemented
55C4⋊(C31⋊C8)C2211yescharacteristic, complemented
56C4⋊(C31⋊C8)C2211yescharacteristic, complemented
57#11758391C2211yescharacteristic, complemented
58C4×C31⋊C8C2211yescharacteristic, complemented
59C24×C31—21no—
60C2×D4×C31—22no—
61C2×D4×C31—22no—
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C2×D4×C31C2311yescharacteristic
65C22×C4×C31—21no—
66C22×C4×C31—21no—
67C22×C4×C31—21no—
68C22×C4×C31—21no—
69C22×C4×C31C2311yescharacteristic
70C2×C22⋊D31—21no—
71C2×D124C2311yescharacteristic
72C2×C4×D31—21no—
73C2×Dic62—21no—
74C2×Dic62C2311yescharacteristic
75C4⋊C4×C31D411yescharacteristic
76C4⋊C4×C31D411yescharacteristic
77C4⋊C4×C31C2311yescharacteristic
78C4⋊C4×C31C2311yescharacteristic
79C22⋊C4×C31—21no—
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C22⋊C4×C31D411yescharacteristic
85C22⋊C4×C31D411yescharacteristic
86C42×C31—21no—
87C42×C31C2311yescharacteristic
88C42×C31C2311yescharacteristic
89C22⋊Dic31—21no—
90#92480—22no—
91#92480—22no—
92#92479—22no—
93#92479—22no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103C4×Dic31—21no—
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C23×C31—24no—
109C23×C31—21no—
110C23×C31—21no—
111C23×C31—81no—
112C23×C31—81no—
113C23×C31C2×D411yescharacteristic
114C22×D31—21no—
115D4×C31—24no—
116D4×C31—21no—
117D4×C31—21no—
118D4×C31#4112yes—
119D4×C31#4112yes—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—81no—
125C2×C4×C31—81no—
126C2×C4×C31—81no—
127C2×C4×C31—81no—
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2×D411yescharacteristic
130C2×C4×C31C2×D411yescharacteristic
131C2×C4×C31C2×D411yescharacteristic
132C2×C4×C31C2×D411yescharacteristic
133C2×C4×C31C2411yescharacteristic
134C22⋊D31—81no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138D124—21no—
139D124—21no—
140C4×D31—81no—
141Dic62—21no—
142Dic62—21no—
143Dic62—81no—
144C31⋊C8—21no—
145C31⋊C8—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3118—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—22no—
151C22×C31—22no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—41no—
155C22×C31—41no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—84no—
159C22×C31C22×D411yescharacteristic
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—21no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31C2×#4111yescharacteristic
172Dic31—41no—
173Dic31—41no—
174Dic31—41no—
175#542—311no—
176#518D3111yescharacteristic, complemented
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×SD16—311no—
188C4×D8—311no—
189#433—311no—
190C2×C31—41no—
191C2×C31—42no—
192C2×C31—42no—
193C2×C31#52511yescharacteristic
194C2×C31#57611yescharacteristic
195C2×C31#57711yescharacteristic
196D31—81no—
197C22×D4C2×D3111yescharacteristic
198C2×SD16—311no—
199C2×SD16—311no—
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×Q8—311no—
211C4×D4—21no—
212C4×D4—21no—
213C4×D4—311no—
214C4×D4C2×D3111yescharacteristic
215C4×D4C2×D3111yescharacteristic
216C4×D4C2×D3111yescharacteristic
217C4×D4C2×D3111yescharacteristic
218#117C2×D3111yescharacteristic
219#117C2×D3111yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222#107—311no—
223#107—311no—
224#106—311no—
225#106—311no—
226C4⋊C8—311no—
227C4⋊C8—311no—
228#103—311no—
229#103—311no—
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102—311no—
235#102—311no—
236C22⋊C8—311no—
237C22⋊C8—311no—
238#97—311no—
239C4×C8—311no—
240C31#311811yescharacteristic, complemented, Sylow
241C24—21no—
242C2×Q8—311no—
243C2×Q8—621no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—311no—
248C2×D4—621no—
249C2×D4C22×D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—621no—
256C22×C4C22×D3111yescharacteristic
257SD16—622no—
258SD16—622no—
259D8—622no—
260D8—622no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8—311no—
264C2×C8—311no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4C22⋊D3111yescharacteristic
271C4⋊C4C22⋊D3111yescharacteristic
272C4⋊C4C22×D3111yescharacteristic
273C4⋊C4C22×D3111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4C22⋊D3111yescharacteristic
285C22⋊C4C22⋊D3111yescharacteristic
286C42—21no—
287C42—621no—
288C42C22×D3111yescharacteristic
289C42C22×D3111yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—621no—
296C23C2×C22⋊D3111yescharacteristic
297Q8—621no—
298Q8—621no—
299Q8—2481no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—621no—
304D4—621no—
305D4—2481no—
306D4#9249512yes—
307D4#9249512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—2481no—
320C2×C4C2×C22⋊D3111yescharacteristic
321C2×C4C2×C22⋊D3111yescharacteristic
322C2×C4C2×C22⋊D3111yescharacteristic
323C2×C4C2×C22⋊D3111yescharacteristic
324C2×C4C2×C22⋊D3111yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—621no—
327C8—621no—
328C8—621no—
329C8—621no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—22no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—1241no—
341C22—1241no—
342C22—1241no—
343C22C22×C22⋊D3111yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—1241no—
352C4—1241no—
353C4—1241no—
354C4C2×#9249511yescharacteristic
355C4C2×#9249511yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—2481no—
360C2#1452156011yescharacteristic
361C2#1452185211yescharacteristic
362C2#1452186011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#518C2
socleC22×C31C22×D4
prime radical#14521183C2
hypercenter#518D31
hypocenterC31#3118
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14521670C2semidirect
2. #14521390C2semidirect
3. #14521373C2semidirect
4. #14521339C2semidirect
5. #14521329C2semidirect
6. #14521264C2semidirect
7. #14521264C2semidirect
8. #14521200C2semidirect
10. #14521159C2semidirect
11. #14521149C2semidirect
12. C4×#92480C2semidirect
13. C4×#92479C2semidirect
14. #14521110C2semidirect
15. C31×#518C2semidirect
37. #11758452C22semidirect
38. C4×D124C22semidirect
39. #11758446C22semidirect
40. C4×Dic62C22semidirect
47. #11758398C22semidirect
48. #11758398C22semidirect
49. #11758397C22semidirect
50. #11758397C22semidirect
51. #11758396C22semidirect
52. #11758396C22semidirect
53. #11758395C22semidirect
54. #11758395C22semidirect
55. C4⋊(C31⋊C8)C22semidirect
56. C4⋊(C31⋊C8)C22semidirect
57. #11758391C22semidirect
58. C4×C31⋊C8C22semidirect
176. #518D31semidirect
240. C31#3118semidirect

Maximal subgroups

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

subgroupindex
#145216702
#145213902
#145213732
#145213392
#145213292
#145212642
#145212002
#145211832
#145211592
#145211492
C4×#924802
C4×#924792
#145211102
C31×#5182
#311831