Finite Group Databasebeta

← #16831330

Subgroups — #16831330

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#14271852C211yesmaximal, characteristic, complemented
2#14271810C211yesmaximal, characteristic
3#14271516C211yesmaximal, characteristic, complemented
4#14271495C211yesmaximal, characteristic, complemented
5#14271466C211yesmaximal, characteristic, complemented
6#14271405C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271384C211yesmaximal, characteristic, complemented
9#14271327C211yesmaximal, characteristic, complemented
10#14271315C211yesmaximal, characteristic, complemented
11#14271250C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13#14271157C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#482C211yesmaximal, characteristic, complemented
16C2×D4×D29C2211yescharacteristic
17C2×#90805C2211yescharacteristic
18C29×#121C2211yescharacteristic
19C29×#117C2211yescharacteristic, complemented
20#11745300—21no—
21#11745299—21no—
22#11745298C2211yescharacteristic
23C2×#90783C2211yescharacteristic
24C4×C22⋊D29C2211yescharacteristic
25#11745286C2211yescharacteristic, complemented
26C22×#6597C2211yescharacteristic, complemented
27C2×Dic116C2211yescharacteristic, complemented
28C2×#90773C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic
30#11745259C2211yescharacteristic
31#11745259C2211yescharacteristic
32#11745255C2211yescharacteristic
33C4⋊C4×D29C2211yescharacteristic
34#11745252C2211yescharacteristic, complemented
35#11745249C2211yescharacteristic, complemented
36#11745245—21no—
37#11745245—21no—
38C22⋊C4×D29—21no—
39#11745241—21no—
40#11745234—21no—
41#11745232—21no—
42C29×#107C2211yescharacteristic, complemented
43C29×#106C2211yescharacteristic, complemented
44C29×#102C2211yescharacteristic
45C29×#102C2211yescharacteristic
46C29×C22⋊C8C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745168C2211yescharacteristic
50#11745164C2211yescharacteristic, complemented
51#11745162C2211yescharacteristic, complemented
52C8×Dic29C2211yescharacteristic, complemented
53#11745158C2211yescharacteristic, complemented
54#11745158C2211yescharacteristic, complemented
55#11745158C2211yescharacteristic, complemented
56#11745157C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745156C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29—21no—
61C2×D4×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C2×C22⋊D29D411yescharacteristic
66D4×D29—22no—
67D4×D29—41no—
68#90805—22no—
69#90805—41no—
70C2×D116C2311yescharacteristic
71C2×C4×D29—21no—
72C2×C4×D29—21no—
73C2×C4×D29—21no—
74C2×C4×D29C2311yescharacteristic
75C2×Dic58C2311yescharacteristic
76C2×Dic58C2311yescharacteristic
77C2×C8×C29C2311yescharacteristic
78C2×C8×C29C2311yescharacteristic
79C4⋊C4×C29C2311yescharacteristic
80C4⋊C4×C29C2311yescharacteristic
81C4⋊C4×C29C2311yescharacteristic
82C22⋊C4×C29—21no—
83C22⋊C4×C29—21no—
84C42×C29—21no—
85C22⋊Dic29—21no—
86C22⋊Dic29—21no—
87C22⋊Dic29—21no—
88C22⋊Dic29D411yescharacteristic
89#90783—41no—
90#90781—21no—
91#90781—21no—
92#90781—21no—
93#90781D411yescharacteristic
94C4⋊Dic29—21no—
95C4⋊Dic29—21no—
96C4⋊Dic29—21no—
97C4⋊Dic29C2311yescharacteristic
98#90779—21no—
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779D411yescharacteristic
103C4×Dic29—21no—
104C4×Dic29C2311yescharacteristic
105C2×#6597—41no—
106C2×#6597C2311yescharacteristic
107C2×#6597C2311yescharacteristic
108Dic116—41no—
109#90773—22no—
110C8×D29—41no—
111C23×C29—21no—
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29—42no—
115C22×D29—42no—
116C22×D29—81no—
117C22×D29C2×D411yescharacteristic
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—81no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—22no—
129C22⋊D29—42no—
130C22⋊D29—42no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29C2×D411yescharacteristic
135C2×Dic29C2×D411yescharacteristic
136C2×Dic29C2×D411yescharacteristic
137D116—21no—
138D116#4112yes—
139C4×D29—21no—
140C4×D29—21no—
141C4×D29—42no—
142C4×D29—42no—
143C4×D29—81no—
144Dic58—21no—
145Dic58—21no—
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#482D2911yescharacteristic, complemented
184#478—291no—
185#467—291no—
186#465—291no—
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×SD16—291no—
206C22×C8—291no—
207C22×C8—291no—
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⋊Q8—291no—
217#121—581no—
218#121C2×D2911yescharacteristic
219#120—581no—
220C4×Q8—291no—
221C4×D4—291no—
222C4×D4—291no—
223#117—581no—
224#117C2×D2911yescharacteristic, complemented
225C2×C4⋊C4—291no—
226C2×C22⋊C4—581no—
227#107C2×D2911yescharacteristic, complemented
228#106—291no—
229#106C2×D2911yescharacteristic, complemented
230C4⋊C8—291no—
231#103—291no—
232#103—291no—
233#103—291no—
234#103—291no—
235#102—291no—
236#102—291no—
237#102—291no—
238#102—291no—
239#102C2×D2911yescharacteristic
240#102C2×D2911yescharacteristic
241C22⋊C8—291no—
242C22⋊C8C2×D2911yescharacteristic, complemented
243C4×C8—291no—
244C29#329611yescharacteristic, complemented, Sylow
245C24—581no—
246#41—582no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8—291no—
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—582no—
265SD16—1161no—
266C2×C8—291no—
267C2×C8—291no—
268C2×C8—1161no—
269C2×C8—1161no—
270C2×C8C22×D2911yescharacteristic
271C2×C8C22×D2911yescharacteristic
272C4⋊C4—291no—
273C4⋊C4—291no—
274C4⋊C4—581no—
275C4⋊C4—581no—
276C4⋊C4—581no—
277C4⋊C4—581no—
278C4⋊C4—581no—
279C4⋊C4—581no—
280C4⋊C4—581no—
281C4⋊C4C22×D2911yescharacteristic
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—21no—
295C42—291no—
296C42—581no—
297C23—21no—
298C23—291no—
299C23—581no—
300C23—1162no—
301C23—1162no—
302C23—2321no—
303C23D4×D2911yescharacteristic
304Q8—581no—
305Q8—581no—
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#41×D2911yescharacteristic
363C4#1174536411yescharacteristic
364C2—41no—
365C2—81no—
366C2—582no—
367C2—1162no—
368C2#1427180511yescharacteristic
369C2#135×D2911yescharacteristic
370C2#1427197311yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#482C2
socleC22×C29C22×D4
prime radical#14271810C2
hypercenter#482D29
hypocenterC29#3296
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14271852C2semidirect
3. #14271516C2semidirect
4. #14271495C2semidirect
5. #14271466C2semidirect
6. #14271405C2semidirect
7. #14271390C2semidirect
8. #14271384C2semidirect
9. #14271327C2semidirect
10. #14271315C2semidirect
11. #14271250C2semidirect
12. #14271226C2semidirect
13. #14271157C2semidirect
14. #102×D29C2semidirect
15. C29×#482C2semidirect
19. C29×#117C22semidirect
25. #11745286C22semidirect
26. C22×#6597C22semidirect
27. C2×Dic116C22semidirect
34. #11745252C22semidirect
35. #11745249C22semidirect
42. C29×#107C22semidirect
43. C29×#106C22semidirect
46. C29×C22⋊C8C22semidirect
50. #11745164C22semidirect
51. #11745162C22semidirect
52. C8×Dic29C22semidirect
53. #11745158C22semidirect
54. #11745158C22semidirect
55. #11745158C22semidirect
58. #11745156C22semidirect
183. #482D29semidirect
224. #117C2×D29semidirect
227. #107C2×D29semidirect
229. #106C2×D29semidirect
242. C22⋊C8C2×D29semidirect
244. C29#3296semidirect

Maximal subgroups

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

subgroupindex
#142718522
#142718102
#142715162
#142714952
#142714662
#142714052
#142713902
#142713842
#142713272
#142713152
#142712502
#142712262
#142711572
#102×D292
C29×#4822
#329629