Finite Group Databasebeta

← #16831329

Subgroups — #16831329

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#14271853C211yesmaximal, characteristic, complemented
2#14271809C211yesmaximal, characteristic
3#14271518C211yesmaximal, characteristic, complemented
4#14271494C211yesmaximal, characteristic, complemented
5#14271488C211yesmaximal, characteristic, complemented
6#14271464C211yesmaximal, characteristic, complemented
7#14271404C211yesmaximal, characteristic, complemented
8#14271392C211yesmaximal, characteristic, complemented
9#14271386C211yesmaximal, characteristic, complemented
10#14271327C211yesmaximal, characteristic, complemented
11#14271316C211yesmaximal, characteristic, complemented
12C4×#90773C211yesmaximal, characteristic, complemented
13#14271160C211yesmaximal, characteristic, complemented
14C2×#11745169C211yesmaximal, characteristic, complemented
15C8×D4×C29C211yesmaximal, characteristic, complemented
16C2×#90805C2211yescharacteristic
17C22×D116C2211yescharacteristic
18C22×C8×C29C2211yescharacteristic
19C22×C8×C29C2211yescharacteristic, complemented
20C4×D4×C29C2211yescharacteristic
21#11745299—21no—
22#11745297—21no—
23#11745292C2211yescharacteristic
24#11745288C2211yescharacteristic, complemented
25C2×C4⋊Dic29C2211yescharacteristic
26#11745286C2211yescharacteristic
27#11745286C2211yescharacteristic
28#11745286C2211yescharacteristic, complemented
29C2×Dic116C2211yescharacteristic, complemented
30C2×#90773C2211yescharacteristic
31C2×#90773C2211yescharacteristic
32#11745256—21no—
33#11745251—21no—
34#11745246—21no—
35C22⋊C4×D29—21no—
36#11745241—21no—
37#11745239—21no—
38#11745237C2211yescharacteristic
39C4×D116C2211yescharacteristic
40#11745232C2211yescharacteristic, complemented
41C4×Dic58C2211yescharacteristic, complemented
42C29×C4⋊C8C2211yescharacteristic, complemented
43C29×C22⋊C8C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic, complemented
45C4×C8×C29C2211yescharacteristic, complemented
46#11745169C2211yescharacteristic
47#11745169C2211yescharacteristic
48#11745169C2211yescharacteristic
49#11745169C2211yescharacteristic
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745166C2211yescharacteristic, complemented
53#11745165C2211yescharacteristic, complemented
54#11745165C2211yescharacteristic, complemented
55#11745164C2211yescharacteristic, complemented
56#11745164C2211yescharacteristic, complemented
57#11745164C2211yescharacteristic, complemented
58#11745164C2211yescharacteristic, complemented
59C23×D29—21no—
60C2×D4×C29D411yescharacteristic
61C22×C4×C29C2311yescharacteristic
62C22×C4×C29C2311yescharacteristic
63C2×C22⋊D29—21no—
64C2×C22⋊D29—21no—
65C22×Dic29—21no—
66#90805—22no—
67#90805—41no—
68C2×D116—22no—
69C2×D116—21no—
70C2×D116—41no—
71C2×D116C2311yescharacteristic
72C2×D116C2311yescharacteristic
73C2×C4×D29—21no—
74C2×C4×D29—21no—
75C2×Dic58C2311yescharacteristic
76C2×Dic58C2311yescharacteristic
77C2×C8×C29—41no—
78C2×C8×C29—41no—
79C2×C8×C29C2311yescharacteristic
80C2×C8×C29C2311yescharacteristic
81C2×C8×C29C2311yescharacteristic
82C2×C8×C29C2311yescharacteristic
83C4⋊C4×C29D411yescharacteristic
84C22⋊C4×C29D411yescharacteristic
85C22⋊C4×C29D411yescharacteristic
86C42×C29C2311yescharacteristic
87C22⋊Dic29—21no—
88C22⋊Dic29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91#90781—21no—
92#90781—21no—
93#90781—21no—
94#90781—21no—
95C4⋊Dic29—21no—
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99C4⋊Dic29C2311yescharacteristic
100#90779—21no—
101#90779—21no—
102#90779—21no—
103#90779—21no—
104#90779—21no—
105#90779—21no—
106C4×Dic29—21no—
107C4×Dic29—21no—
108Dic116—41no—
109#90773—22no—
110#90773—41no—
111C23×C29C2×D411yescharacteristic
112C23×C29C2×D411yescharacteristic
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—42no—
116C22×D29—42no—
117C22×D29—81no—
118D4×C29—22no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29C2×D411yescharacteristic
124C2×C4×C29C2×D411yescharacteristic
125C2×C4×C29C2×D411yescharacteristic
126C2×C4×C29C2×D411yescharacteristic
127C2×C4×C29C2411yescharacteristic
128C22⋊D29—42no—
129C22⋊D29—81no—
130C2×Dic29—21no—
131C2×Dic29—21no—
132C2×Dic29—21no—
133C2×Dic29—21no—
134C2×Dic29—21no—
135C2×Dic29—21no—
136C2×Dic29—42no—
137D116—21no—
138D116—21no—
139D116—21no—
140D116—42no—
141D116#4112yes—
142C4×D29—42no—
143C4×D29—81no—
144Dic58—21no—
145Dic58—21no—
146Dic58—21no—
147Dic58—21no—
148C8×C29—21no—
149C8×C29—21no—
150C8×C29—21no—
151C8×C29—21no—
152#3296—291nomaximal, Sylow
153C22×C29—21no—
154C22×C29—21no—
155C22×C29—21no—
156C22×C29—21no—
157C22×C29—21no—
158C22×C29#13512yes—
159C22×C29C22×D411yescharacteristic
160C2×D29—22no—
161C2×D29—41no—
162C2×D29—41no—
163C2×D29—41no—
164C2×D29—41no—
165C2×D29—41no—
166C2×D29—84no—
167C4×C29—21no—
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29C2×#4111yescharacteristic
172C4×C29H(5,𝔽2)11yescharacteristic
173Dic29—41no—
174Dic29—41no—
175Dic29—41no—
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#465—291no—
187#464—291no—
188#452—291no—
189#450—291no—
190C4×SD16—291no—
191C8×D4D2911yescharacteristic, complemented
192#416—291no—
193C2×#102—291no—
194C2×C29—22no—
195C2×C29—41no—
196C2×C29#54611yescharacteristic
197C2×C29C2×#13511yescharacteristic
198C2×C29#57711yescharacteristic
199D29—42no—
200D29—81no—
201C2×#41—291no—
202C22×D4—291no—
203C2×Q16—291no—
204C2×SD16—291no—
205C2×SD16—291no—
206C22×C8C2×D2911yescharacteristic
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⋊Q8—291no—
217#121—291no—
218#121—581no—
219#120—581no—
220C4×Q8—291no—
221C4×D4—291no—
222C4×D4C2×D2911yescharacteristic
223#117—291no—
224#117—581no—
225C2×C4⋊C4—291no—
226C2×C22⋊C4—581no—
227#107—291no—
228#106—291no—
229#106—291no—
230C4⋊C8C2×D2911yescharacteristic, complemented
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#102—291no—
240#102—291no—
241C22⋊C8C2×D2911yescharacteristic
242C22⋊C8C2×D2911yescharacteristic, complemented
243C4×C8C2×D2911yescharacteristic, complemented
244C29#329611yescharacteristic, complemented, Sylow
245C24—581no—
246#41—582no—
247#41—1161no—
248C2×Q8—291no—
249C2×Q8—291no—
250C2×D4—291no—
251C2×D4—291no—
252C2×D4—582no—
253C2×D4—581no—
254C2×D4—581no—
255C2×D4—581no—
256C2×D4—1161no—
257C2×D4D11611yescharacteristic
258C22×C4—581no—
259C22×C4—581no—
260C22×C4—581no—
261C22×C4C22×D2911yescharacteristic
262C22×C4C22×D2911yescharacteristic
263Q16—1161no—
264SD16—582no—
265SD16—1161no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8C22×D2911yescharacteristic
269C2×C8C22×D2911yescharacteristic
270C2×C8C22×D2911yescharacteristic
271C2×C8C22×D2911yescharacteristic
272C4⋊C4—291no—
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⋊C4—581no—
283C4⋊C4D11611yescharacteristic
284C22⋊C4—581no—
285C22⋊C4—581no—
286C22⋊C4—581no—
287C22⋊C4—581no—
288C22⋊C4—581no—
289C22⋊C4—581no—
290C22⋊C4—581no—
291C22⋊C4—581no—
292C22⋊C4D11611yescharacteristic
293C22⋊C4D11611yescharacteristic
294C42—581no—
295C42—581no—
296C42C22×D2911yescharacteristic
297C23—581no—
298C23—581no—
299C23—1162no—
300C23—1162no—
301C23—2321no—
302C23C2×D11611yescharacteristic
303C23C2×D11611yescharacteristic
304Q8—581no—
305Q8—581no—
306Q8—581no—
307Q8—581no—
308D4—22no—
309D4—292no—
310D4—581no—
311D4—581no—
312D4—581no—
313D4—1162no—
314D4—1162no—
315D4—2321no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—581no—
321C2×C4—581no—
322C2×C4—581no—
323C2×C4—581no—
324C2×C4—581no—
325C2×C4—581no—
326C2×C4—1162no—
327C2×C4—1162no—
328C2×C4—2321no—
329C2×C4C2×D11611yescharacteristic
330C2×C4C2×D11611yescharacteristic
331C2×C4C2×D11611yescharacteristic
332C2×C4C2×D11611yescharacteristic
333C2×C4C23×D2911yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—582no—
344C22—1161no—
345C22—1161no—
346C22—1161no—
347C22—1161no—
348C22—1161no—
349C22—2324no—
350C22#1174526612yes—
351C22C22×D11611yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—1161no—
357C4—1161no—
358C4—1161no—
359C4—1161no—
360C4—1161no—
361C4—1161no—
362C4#1174535911yescharacteristic
363C4#41×D2911yescharacteristic
364C2—22no—
365C2—41no—
366C2—1162no—
367C2—2321no—
368C2#1427180811yescharacteristic
369C2C2×#1174526611yescharacteristic
370C2#1427197511yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC8×D4×C29C2
socleC22×C29C22×D4
prime radical#14271809C2
hypercenterC8×D4D29
hypocenterC29#3296
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14271853C2semidirect
3. #14271518C2semidirect
4. #14271494C2semidirect
5. #14271488C2semidirect
6. #14271464C2semidirect
7. #14271404C2semidirect
8. #14271392C2semidirect
9. #14271386C2semidirect
10. #14271327C2semidirect
11. #14271316C2semidirect
12. C4×#90773C2semidirect
13. #14271160C2semidirect
14. C2×#11745169C2semidirect
15. C8×D4×C29C2semidirect
19. C22×C8×C29C22semidirect
24. #11745288C22semidirect
28. #11745286C22semidirect
29. C2×Dic116C22semidirect
40. #11745232C22semidirect
41. C4×Dic58C22semidirect
42. C29×C4⋊C8C22semidirect
44. C29×C22⋊C8C22semidirect
45. C4×C8×C29C22semidirect
52. #11745166C22semidirect
53. #11745165C22semidirect
54. #11745165C22semidirect
55. #11745164C22semidirect
56. #11745164C22semidirect
57. #11745164C22semidirect
58. #11745164C22semidirect
191. C8×D4D29semidirect
207. C22×C8C2×D29semidirect
230. C4⋊C8C2×D29semidirect
242. C22⋊C8C2×D29semidirect
243. C4×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
#142718532
#142718092
#142715182
#142714942
#142714882
#142714642
#142714042
#142713922
#142713862
#142713272
#142713162
C4×#907732
#142711602
C2×#117451692
C8×D4×C292
#329629