Finite Group Databasebeta

← #16831322

Subgroups — #16831322

Order 3712.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271847C211yesmaximal, characteristic, complemented
2#14271810C211yesmaximal, characteristic
3#14271516C211yesmaximal, characteristic, complemented
4#14271495C211yesmaximal, characteristic, complemented
5#14271484C211yesmaximal, characteristic, complemented
6#14271462C211yesmaximal, characteristic, complemented
7#14271403C211yesmaximal, characteristic, complemented
8#14271383C211yesmaximal, characteristic, complemented
9#14271323C211yesmaximal, characteristic, complemented
10#14271312C211yesmaximal, characteristic, complemented
11#14271248C211yesmaximal, characteristic, complemented
12C8×C22⋊D29C211yesmaximal, characteristic, complemented
13#14271160C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#465C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic, complemented
20C29×C22⋊Q8C2211yescharacteristic, complemented
21C29×#121C2211yescharacteristic
22#11745308C2211yescharacteristic
23Q8×Dic29C2211yescharacteristic, complemented
24C2×#90785C2211yescharacteristic, complemented
25C2×#90784C2211yescharacteristic
26#11745300—21no—
27#11745299—21no—
28#11745298C2211yescharacteristic
29C4×C22⋊D29C2211yescharacteristic
30#11745288C2211yescharacteristic, complemented
31C2×C8×D29C2211yescharacteristic
32#11745259C2211yescharacteristic
33#11745255C2211yescharacteristic
34#11745254—21no—
35C4⋊C4×D29C2211yescharacteristic
36#11745252C2211yescharacteristic, complemented
37#11745251—21no—
38#11745245—21no—
39#11745245—21no—
40C22⋊C4×D29—21no—
41#11745241—21no—
42C29×#106C2211yescharacteristic, complemented
43C29×#103C2211yescharacteristic, complemented
44C29×#102C2211yescharacteristic
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47C22⋊#6597C2211yescharacteristic, complemented
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745168C2211yescharacteristic
51#11745164C2211yescharacteristic, complemented
52#11745164C2211yescharacteristic, complemented
53#11745162C2211yescharacteristic, complemented
54C8×Dic29C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic
57#11745156C2211yescharacteristic, complemented
58#11745155C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×D4×C29—21no—
62C2×D4×C29C2311yescharacteristic
63C22×C4×C29C2311yescharacteristic
64C2×C22⋊D29—21no—
65C2×C22⋊D29—21no—
66C2×C22⋊D29D411yescharacteristic
67D4×D29—22no—
68D4×D29—41no—
69#90805—22no—
70#90805—41no—
71C2×D116C2311yescharacteristic
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×C4×D29C2311yescharacteristic
76C2×Dic58C2311yescharacteristic
77SD16×C29—41no—
78C2×C8×C29—41no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C4⋊C4×C29—21no—
82C4⋊C4×C29C2311yescharacteristic
83C4⋊C4×C29C2311yescharacteristic
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29D411yescharacteristic
90#90785—41no—
91#90784—22no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95#90781D411yescharacteristic
96C4⋊Dic29—21no—
97C4⋊Dic29—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779D411yescharacteristic
105C4×Dic29—21no—
106C4×Dic29—21no—
107C4×Dic29C2311yescharacteristic
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C8×D29—41no—
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29—42no—
115C22×D29—42no—
116C22×D29—81no—
117C22×D29C2×D411yescharacteristic
118Q8×C29—21no—
119Q8×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—81no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29C2×D411yescharacteristic
129C2×C4×C29C2411yescharacteristic
130C22⋊D29—22no—
131C22⋊D29—42no—
132C22⋊D29—42no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29C2×D411yescharacteristic
137C2×Dic29C2×D411yescharacteristic
138C2×Dic29C2×D411yescharacteristic
139D116—21no—
140D116#4112yes—
141C4×D29—21no—
142C4×D29—21no—
143C4×D29—42no—
144C4×D29—42no—
145C4×D29—81no—
146Dic58—21no—
147Dic58—21no—
148C8×C29—21no—
149C8×C29—21no—
150#6597—21no—
151#6597—21no—
152#3296—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—41no—
157C22×C29—41no—
158C22×C29—41no—
159C22×C29C22×D411yescharacteristic
160C2×D29—21no—
161C2×D29—21no—
162C2×D29—22no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—84no—
166C2×D29#13512yes—
167C4×C29—21no—
168C4×C29—41no—
169C4×C29—41no—
170C4×C29—41no—
171C4×C29C2×#4111yescharacteristic
172C4×C29H(5,𝔽2)11yescharacteristic
173Dic29—21no—
174Dic29—21no—
175Dic29—21no—
176Dic29—41no—
177Dic29—41no—
178Dic29—41no—
179#552—291no—
180#546—291no—
181#488—291no—
182#483—291no—
183#482—291no—
184#478—291no—
185#467—291no—
186#465D2911yescharacteristic, complemented
187#464—291no—
188#452—291no—
189#450—291no—
190C4×SD16—291no—
191C8×D4—291no—
192#416—291no—
193C2×#102—291no—
194C2×C29—41no—
195C2×C29—81no—
196C2×C29#54611yescharacteristic
197C2×C29C2×#13511yescharacteristic
198C2×C29#57711yescharacteristic
199D29—22no—
200D29—42no—
201C2×#41—291no—
202C22×D4—291no—
203C2×Q16—291no—
204C2×SD16—291no—
205C2×SD16C2×D2911yescharacteristic
206C22×C8—291no—
207C22×C8C2×D2911yescharacteristic, complemented
208#126—581no—
209#125—291no—
210#125—581no—
211#124—291no—
212#123—581no—
213#123—581no—
214C22⋊Q8—291no—
215C22⋊Q8—291no—
216C22⋊Q8C2×D2911yescharacteristic, complemented
217#121—581no—
218#121C2×D2911yescharacteristic
219#120—581no—
220C4×Q8—291no—
221C4×D4—291no—
222C4×D4—291no—
223#117—291no—
224#117—581no—
225C2×C4⋊C4—291no—
226C2×C22⋊C4—581no—
227#107—291no—
228#106—291no—
229#106C2×D2911yescharacteristic, complemented
230C4⋊C8—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103C2×D2911yescharacteristic, complemented
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102—291no—
240#102C2×D2911yescharacteristic
241C22⋊C8—291no—
242C22⋊C8—291no—
243C4×C8—291no—
244C29#329611yescharacteristic, complemented, Sylow
245C24—581no—
246#41—582no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8C22×D2911yescharacteristic
250C2×D4—21no—
251C2×D4—291no—
252C2×D4—291no—
253C2×D4—581no—
254C2×D4—582no—
255C2×D4—581no—
256C2×D4—1161no—
257C2×D4C22×D2911yescharacteristic
258C22×C4—291no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4—581no—
262C22×C4C22×D2911yescharacteristic
263Q16—1161no—
264SD16—41no—
265SD16—582no—
266C2×C8—41no—
267C2×C8—291no—
268C2×C8—291no—
269C2×C8—1161no—
270C2×C8C22×D2911yescharacteristic
271C2×C8C22×D2911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—291no—
274C4⋊C4—291no—
275C4⋊C4—291no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4—581no—
282C4⋊C4C22×D2911yescharacteristic
283C4⋊C4C22×D2911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—291no—
287C22⋊C4—291no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4—581no—
293C22⋊C4—581no—
294C42—291no—
295C42—581no—
296C42—581no—
297C23—21no—
298C23—291no—
299C23—581no—
300C23—1162no—
301C23—1162no—
302C23—2321no—
303C23D4×D2911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—581no—
307Q8—581no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—292no—
312D4—582no—
313D4—581no—
314D4—1162no—
315D4—1162no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—291no—
322C2×C4—291no—
323C2×C4—291no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—581no—
327C2×C4—581no—
328C2×C4—581no—
329C2×C4—1162no—
330C2×C4—1162no—
331C2×C4—2321no—
332C2×C4D4×D2911yescharacteristic
333C2×C4C23×D2911yescharacteristic
334C8—21no—
335C8—21no—
336C8—581no—
337C8—581no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—292no—
345C22—581no—
346C22—581no—
347C22—582no—
348C22—1161no—
349C22—1161no—
350C22—2324no—
351C22C2×D4×D2911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—581no—
357C4—581no—
358C4—581no—
359C4—1161no—
360C4—1161no—
361C4—1161no—
362C4#1174535911yescharacteristic
363C4#41×D2911yescharacteristic
364C2—41no—
365C2—81no—
366C2—582no—
367C2—1162no—
368C2#1427180211yescharacteristic
369C2#135×D2911yescharacteristic
370C2#1427196911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#465C2
socleC22×C29C22×D4
prime radical#14271810C2
hypercenter#465D29
hypocenterC29#3296
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14271847C2semidirect
3. #14271516C2semidirect
4. #14271495C2semidirect
5. #14271484C2semidirect
6. #14271462C2semidirect
7. #14271403C2semidirect
8. #14271383C2semidirect
9. #14271323C2semidirect
10. #14271312C2semidirect
11. #14271248C2semidirect
12. C8×C22⋊D29C2semidirect
13. #14271160C2semidirect
14. #102×D29C2semidirect
15. C29×#465C2semidirect
19. C22×C8×C29C22semidirect
20. C29×C22⋊Q8C22semidirect
23. Q8×Dic29C22semidirect
24. C2×#90785C22semidirect
30. #11745288C22semidirect
36. #11745252C22semidirect
42. C29×#106C22semidirect
43. C29×#103C22semidirect
47. C22⋊#6597C22semidirect
51. #11745164C22semidirect
52. #11745164C22semidirect
53. #11745162C22semidirect
54. C8×Dic29C22semidirect
55. #11745158C22semidirect
57. #11745156C22semidirect
58. #11745155C22semidirect
186. #465D29semidirect
207. C22×C8C2×D29semidirect
216. C22⋊Q8C2×D29semidirect
229. #106C2×D29semidirect
234. #103C2×D29semidirect
244. C29#3296semidirect

Maximal subgroups

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

subgroupindex
#142718472
#142718102
#142715162
#142714952
#142714842
#142714622
#142714032
#142713832
#142713232
#142713122
#142712482
C8×C22⋊D292
#142711602
#102×D292
C29×#4652
#329629