Finite Group Databasebeta

← #16855898

Subgroups — #16855898

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#14521672C211yesmaximal, characteristic, complemented
2#14521523C211yesmaximal, characteristic, complemented
3#14521373C211yesmaximal, characteristic, complemented
4#14521338C211yesmaximal, characteristic, complemented
5#14521328C211yesmaximal, characteristic, complemented
6#14521267C211yesmaximal, characteristic, complemented
7#14521267C211yesmaximal, characteristic, complemented
8#14521199C211yesmaximal, characteristic, complemented
9#14521185C211yesmaximal, characteristic
10#14521160C211yesmaximal, characteristic, complemented
11#14521152C211yesmaximal, characteristic, complemented
12#14521134C211yesmaximal, characteristic, complemented
13#14521131C211yesmaximal, characteristic, complemented
14#14521107C211yesmaximal, characteristic, complemented
15C31×#485C211yesmaximal, characteristic, complemented
16C22×D124C2211yescharacteristic
17C31×C22⋊Q8C2211yescharacteristic
18C31×#117C2211yescharacteristic
19#11758524C2211yescharacteristic, complemented
20Q8×Dic31C2211yescharacteristic, complemented
21C2×#92481C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23#11758507C2211yescharacteristic
24#11758503C2211yescharacteristic
25C2×D248C2211yescharacteristic
26C2×D248C2211yescharacteristic
27#11758475—21no—
28#11758474—21no—
29#11758470C2211yescharacteristic
30#11758470C2211yescharacteristic
31#11758470C2211yescharacteristic
32#11758470C2211yescharacteristic
33#11758470C2211yescharacteristic, complemented
34#11758465C2211yescharacteristic, complemented
35#11758462—21no—
36#11758460—21no—
37C22⋊C4×D31—21no—
38C22⋊C4×D31—21no—
39C4×D124—21no—
40C4×D124—21no—
41C31×#107C2211yescharacteristic, complemented
42C31×#106C2211yescharacteristic, complemented
43C31×#103C2211yescharacteristic, complemented
44C31×#103C2211yescharacteristic, complemented
45C31×C22⋊C8C2211yescharacteristic
46C22⋊(C31⋊C8)C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758403C2211yescharacteristic, complemented
50Dic31⋊C8C2211yescharacteristic, complemented
51Dic31⋊C8C2211yescharacteristic, complemented
52C8×Dic31C2211yescharacteristic, complemented
53#11758397C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic, complemented
56#11758397C2211yescharacteristic, complemented
57#11758396C2211yescharacteristic, complemented
58#11758395C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×Q8×C31C2311yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C2×C22⋊D31—21no—
63C2×D124—21no—
64C2×D124—22no—
65C2×D124—22no—
66C2×D124C2311yescharacteristic
67C2×D124C2311yescharacteristic
68C2×D124C2311yescharacteristic
69C2×C4×D31—21no—
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×C4×D31—21no—
74C2×Dic62—21no—
75C2×C8×C31C2311yescharacteristic
76C2×C8×C31C2311yescharacteristic
77C4⋊C4×C31—21no—
78C4⋊C4×C31C2311yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C4⋊C4×C31C2311yescharacteristic
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C42×C31—21no—
84C22⋊Dic31D411yescharacteristic
85C22⋊Dic31D411yescharacteristic
86#92481—22no—
87#92481—22no—
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)⋊C4—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31D411yescharacteristic
98C4⋊Dic31D411yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100Dic31⋊C4—21no—
101C4×Dic31—21no—
102C4×Dic31C2311yescharacteristic
103C4×Dic31C2311yescharacteristic
104C2×C31⋊C8C2311yescharacteristic
105C2×C31⋊C8C2311yescharacteristic
106D248—22no—
107D248—22no—
108C23×C31C2×D411yescharacteristic
109C22×D31—21no—
110C22×D31—21no—
111C22×D31—24no—
112C22×D31—21no—
113C22×D31—81no—
114C22×D31—81no—
115Q8×C31—21no—
116Q8×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2411yescharacteristic
125C22⋊D31—81no—
126C2×Dic31—21no—
127C2×Dic31C2×D411yescharacteristic
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130C2×Dic31C2×D411yescharacteristic
131D124—24no—
132D124—21no—
133D124—21no—
134D124—21no—
135D124—21no—
136D124#4112yes—
137D124#4112yes—
138C4×D31—81no—
139C4×D31—81no—
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—21no—
150C22×C31—21no—
151C22×C31—21no—
152C22×C31C22×D411yescharacteristic
153C2×D31—22no—
154C2×D31—22no—
155C2×D31—41no—
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—84no—
163C4×C31—21no—
164C4×C31—41no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31—41no—
168C4×C31C2×#4111yescharacteristic
169C4×C31C2×#4111yescharacteristic
170Dic31—21no—
171Dic31—21no—
172Dic31—21no—
173Dic31—21no—
174Dic31—41no—
175#542—311no—
176#518—311no—
177#485D3111yescharacteristic, complemented
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#52511yescharacteristic
192C2×C31#57611yescharacteristic
193C2×C31#57711yescharacteristic
194D31—42no—
195D31—42no—
196D31—81no—
197C22×D4—311no—
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—621no—
208C22⋊Q8C2×D3111yescharacteristic
209#121—311no—
210C4×Q8—311no—
211C4×D4—311no—
212C4×D4—311no—
213C4×D4—311no—
214C4×D4—311no—
215C4×D4—311no—
216C4×D4—621no—
217C4×D4—621no—
218#117—311no—
219#117C2×D3111yescharacteristic
220C2×C22⋊C4—621no—
221C2×C22⋊C4—621no—
222#107—311no—
223#107C2×D3111yescharacteristic, complemented
224#106—311no—
225#106C2×D3111yescharacteristic, complemented
226C4⋊C8—311no—
227C4⋊C8—311no—
228#103C2×D3111yescharacteristic, complemented
229#103C2×D3111yescharacteristic, complemented
230#102—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234#102—311no—
235#102—311no—
236C22⋊C8—311no—
237C22⋊C8C2×D3111yescharacteristic
238#97—311no—
239C4×C8—311no—
240C31#311811yescharacteristic, complemented, Sylow
241C24—621no—
242C2×Q8—621no—
243C2×Q8C22×D3111yescharacteristic
244C2×D4—311no—
245C2×D4—311no—
246C2×D4—311no—
247C2×D4—622no—
248C2×D4—622no—
249C2×D4—621no—
250C2×D4—621no—
251C22×C4—621no—
252C22×C4—621no—
253C22×C4—621no—
254C22×C4—621no—
255C22×C4—621no—
256C22×C4C22×D3111yescharacteristic
257SD16—622no—
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—621no—
270C4⋊C4—621no—
271C4⋊C4C22×D3111yescharacteristic
272C4⋊C4C22×D3111yescharacteristic
273C4⋊C4C22×D3111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—311no—
277C22⋊C4—311no—
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—311no—
289C42—621no—
290C23—624no—
291C23—621no—
292C23—621no—
293C23—621no—
294C23—2481no—
295C23—2481no—
296C23D4×D3111yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—2481no—
300D4—312no—
301D4—312no—
302D4—624no—
303D4—621no—
304D4—621no—
305D4—621no—
306D4—621no—
307D4—2481no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—311no—
315C2×C4—311no—
316C2×C4—311no—
317C2×C4—311no—
318C2×C4—621no—
319C2×C4—2481no—
320C2×C4—2481no—
321C2×C4—2481no—
322C2×C4—2481no—
323C2×C4—2481no—
324C2×C4D4×D3111yescharacteristic
325C2×C4C23×D3111yescharacteristic
326C8—21no—
327C8—21no—
328C8—621no—
329C8—621no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—622no—
334C22—622no—
335C22—1241no—
336C22—1241no—
337C22—1241no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22—1241no—
342C22—2484no—
343C22C2×D4×D3111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—621no—
350C4—621no—
351C4—621no—
352C4—621no—
353C4—1241no—
354C4#41×D3111yescharacteristic
355C4#41×D3111yescharacteristic
356C2—41no—
357C2—1242no—
358C2—1242no—
359C2—2481no—
360C2#1452155711yescharacteristic
361C2#1452185111yescharacteristic
362C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#485C2
socleC22×C31C22×D4
prime radical#14521185C2
hypercenter#485D31
hypocenterC31#3118
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14521672C2semidirect
2. #14521523C2semidirect
3. #14521373C2semidirect
4. #14521338C2semidirect
5. #14521328C2semidirect
6. #14521267C2semidirect
7. #14521267C2semidirect
8. #14521199C2semidirect
10. #14521160C2semidirect
11. #14521152C2semidirect
12. #14521134C2semidirect
13. #14521131C2semidirect
14. #14521107C2semidirect
15. C31×#485C2semidirect
19. #11758524C22semidirect
20. Q8×Dic31C22semidirect
33. #11758470C22semidirect
34. #11758465C22semidirect
41. C31×#107C22semidirect
42. C31×#106C22semidirect
43. C31×#103C22semidirect
44. C31×#103C22semidirect
49. #11758403C22semidirect
50. Dic31⋊C8C22semidirect
51. Dic31⋊C8C22semidirect
52. C8×Dic31C22semidirect
55. #11758397C22semidirect
56. #11758397C22semidirect
57. #11758396C22semidirect
58. #11758395C22semidirect
177. #485D31semidirect
223. #107C2×D31semidirect
225. #106C2×D31semidirect
228. #103C2×D31semidirect
229. #103C2×D31semidirect
240. C31#3118semidirect

Maximal subgroups

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

subgroupindex
#145216722
#145215232
#145213732
#145213382
#145213282
#145212672
#145211992
#145211852
#145211602
#145211522
#145211342
#145211312
#145211072
C31×#4852
#311831