Finite Group Databasebeta

← #16831446

Subgroups — #16831446

Order 3712.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271813C211yesmaximal, characteristic, complemented
2#14271801C211yesmaximal, characteristic, complemented
3#14271524C211yesmaximal, characteristic, complemented
4#14271492C211yesmaximal, characteristic, complemented
5#14271482C211yesmaximal, characteristic, complemented
6#14271451C211yesmaximal, characteristic, complemented
7#14271414C211yesmaximal, characteristic, complemented
8#14271389C211yesmaximal, characteristic, complemented
9#14271380C211yesmaximal, characteristic, complemented
10#14271295C211yesmaximal, characteristic, complemented
11#14271275C211yesmaximal, characteristic, complemented
12#14271237C211yesmaximal, characteristic, complemented
13#14271164C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#449C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#90807—21no—
18C2×D4×D29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic, complemented
20C2×D8×C29C2211yescharacteristic
21C29×#121C2211yescharacteristic, complemented
22#11745309C2211yescharacteristic
23#11745308C2211yescharacteristic
24#11745301—21no—
25#11745300C2211yescharacteristic
26#11745299—21no—
27#11745297—21no—
28D4×Dic29C2211yescharacteristic
29D4×Dic29C2211yescharacteristic, complemented
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745291—21no—
33C4×C22⋊D29C2211yescharacteristic
34C2×#90781—21no—
35C2×C4⋊Dic29C2211yescharacteristic, complemented
36C2×#90777C2211yescharacteristic, complemented
37C2×C8×D29C2211yescharacteristic
38C4⋊C4×D29C2211yescharacteristic
39#11745250C2211yescharacteristic, complemented
40#11745245—21no—
41#11745240—21no—
42C29×#103C2211yescharacteristic, complemented
43C29×#102C2211yescharacteristic
44C29×C22⋊C8C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745183C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic, complemented
50#11745169C2211yescharacteristic
51#11745169C2211yescharacteristic
52#11745168C2211yescharacteristic
53#11745165C2211yescharacteristic, complemented
54#11745165C2211yescharacteristic, complemented
55#11745163C2211yescharacteristic, complemented
56#11745162C2211yescharacteristic, complemented
57#11745157C2211yescharacteristic
58#11745156C2211yescharacteristic, complemented
59C23×D29—21no—
60#41×C29—22no—
61#41×C29—41no—
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—21no—
64C2×D4×C29—21no—
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29—21no—
68C22×C4×C29C2311yescharacteristic
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29D411yescharacteristic
73C22×Dic29—21no—
74C22×Dic29—21no—
75C22×Dic29—21no—
76#90807—44no—
77D4×D29—22no—
78D4×D29—41no—
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C2×C4×D29C2311yescharacteristic
82C2×Dic58—21no—
83SD16×C29—41no—
84D8×C29—22no—
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C4⋊C4×C29C2311yescharacteristic
88C22⋊C4×C29—21no—
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29—21no—
92C22⋊Dic29D411yescharacteristic
93#90782—41no—
94#90781—21no—
95#90781—21no—
96#90781—21no—
97#90781—21no—
98#90781D411yescharacteristic
99C4⋊Dic29—21no—
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102C4⋊Dic29C2311yescharacteristic
103#90779—21no—
104#90779—21no—
105#90779—21no—
106#90779D411yescharacteristic
107C4×Dic29C2311yescharacteristic
108#90777—41no—
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C8×D29—41no—
112C23×C29—21no—
113C23×C29—21no—
114C23×C29C2×D411yescharacteristic
115C22×D29—21no—
116C22×D29—42no—
117C22×D29—42no—
118C22×D29—81no—
119C22×D29C2×D411yescharacteristic
120Q8×C29—21no—
121Q8×C29—21no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—21no—
125D4×C29—42no—
126D4×C29—42no—
127D4×C29#4112yescomplemented
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—42no—
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2411yescharacteristic
135C22⋊D29—22no—
136C22⋊D29—42no—
137C22⋊D29—42no—
138C22⋊D29—81no—
139C2×Dic29—21no—
140C2×Dic29—21no—
141C2×Dic29—21no—
142C2×Dic29—42no—
143C2×Dic29—42no—
144C2×Dic29—81no—
145C2×Dic29C2×D411yescharacteristic
146C2×Dic29C2×D411yescharacteristic
147C2×Dic29C2×D411yescharacteristic
148D116—21no—
149D116—21no—
150C4×D29—21no—
151C4×D29—21no—
152C4×D29—42no—
153Dic58—42no—
154C8×C29—21no—
155C8×C29—21no—
156#6597—21no—
157#6597—21no—
158#3306—291nomaximal, Sylow
159C22×C29—22no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29C22×D411yescharacteristic
169C2×D29—21no—
170C2×D29—21no—
171C2×D29—41no—
172C2×D29—41no—
173C2×D29—41no—
174C2×D29—84no—
175C2×D29AGL(1,ℤ/8)12yes—
176C4×C29—21no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29C2×#4111yescharacteristic
180C4×C29H(5,𝔽2)11yescharacteristic
181Dic29—21no—
182Dic29—21no—
183Dic29—21no—
184Dic29—41no—
185Dic29—41no—
186Dic29—41no—
187#547—291no—
188#546—291no—
189#489—291no—
190#483—291no—
191#481—291no—
192#476—291no—
193#469—291no—
194#465—291no—
195#463—291no—
196#449D2911yescharacteristic, complemented
197#447—291no—
198#442—291no—
199#435—291no—
200#417—291no—
201C2×#102—291no—
202C2×C29—42no—
203C2×C29—41no—
204C2×C29—81no—
205C2×C29#54611yescharacteristic
206C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
207C2×C29#57711yescharacteristic
208D29—22no—
209D29—81no—
210C2×#41—581no—
211C2×#41C2×D2911yescharacteristic
212C22×D4—291no—
213C2×SD16C2×D2911yescharacteristic, complemented
214C2×D8—291no—
215C2×D8C2×D2911yescharacteristic
216C2×M16—291no—
217C22×C8—291no—
218C4⋊Q8—291no—
219#124—291no—
220#123—581no—
221#123—581no—
222#123—581no—
223C22⋊Q8—291no—
224C22⋊Q8—581no—
225#121—291no—
226#121—291no—
227#121—581no—
228#121C2×D2911yescharacteristic, complemented
229#120—581no—
230C4×D4—291no—
231C4×D4—291no—
232C4×D4—291no—
233C2×C4⋊C4—291no—
234C2×C4⋊C4—291no—
235C2×C22⋊C4—581no—
236#106—291no—
237#106—291no—
238#106—291no—
239C4⋊C8—291no—
240#103—291no—
241#103—291no—
242#103C2×D2911yescharacteristic, complemented
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102C2×D2911yescharacteristic
250C22⋊C8—291no—
251C22⋊C8C2×D2911yescharacteristic, complemented
252#97—291no—
253C29#330611yescharacteristic, complemented, Sylow
254C24—581no—
255#41—22no—
256#41—41no—
257#41—1164no—
258C2×Q8—581no—
259C2×Q8C22×D2911yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—291no—
263C2×D4—291no—
264C2×D4—581no—
265C2×D4—582no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—1161no—
269C2×D4C22×D2911yescharacteristic
270C2×D4C22×D2911yescharacteristic
271C22×C4—21no—
272C22×C4—291no—
273C22×C4—581no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4—581no—
277C22×C4C22×D2911yescharacteristic
278SD16—41no—
279D8—22no—
280D8—1161no—
281M16—1161no—
282C2×C8—291no—
283C2×C8—291no—
284C2×C8—1161no—
285C2×C8C22×D2911yescharacteristic
286C2×C8C22×D2911yescharacteristic
287C4⋊C4—291no—
288C4⋊C4—291no—
289C4⋊C4—291no—
290C4⋊C4—291no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4—581no—
295C4⋊C4C22×D2911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—291no—
298C22⋊C4—291no—
299C22⋊C4—581no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4—581no—
305C22⋊C4—581no—
306C42—291no—
307C23—21no—
308C23—21no—
309C23—291no—
310C23—581no—
311C23—1162no—
312C23—1162no—
313C23—2321no—
314C23D4×D2911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1162no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—582no—
324D4—581no—
325D4—581no—
326D4—1162no—
327D4—1162no—
328D4—2321no—
329D4#9080712yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—291no—
336C2×C4—291no—
337C2×C4—291no—
338C2×C4—581no—
339C2×C4—581no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—1162no—
344C2×C4—1162no—
345C2×C4—1162no—
346C2×C4—2321no—
347C2×C4D4×D2911yescharacteristic
348C2×C4C23×D2911yescharacteristic
349C8—21no—
350C8—21no—
351C8—581no—
352C8—581no—
353C22—21no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—292no—
363C22—581no—
364C22—581no—
365C22—1161no—
366C22—1161no—
367C22—1161no—
368C22—2324no—
369C22C2×D4×D2911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—581no—
374C4—581no—
375C4—581no—
376C4—1161no—
377C4—1161no—
378C4—1161no—
379C4C2×#9080711yescharacteristic
380C4#1174535911yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—582no—
385C2—2321no—
386C2#1427180011yescharacteristic
387C2AGL(1,ℤ/8)×D2911yescharacteristic
388C2#1427197011yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#449C2
socleC22×C29C22×D4
hypercenter#449D29
hypocenterC29#3306
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14271813C2semidirect
2. #14271801C2semidirect
3. #14271524C2semidirect
4. #14271492C2semidirect
5. #14271482C2semidirect
6. #14271451C2semidirect
7. #14271414C2semidirect
8. #14271389C2semidirect
9. #14271380C2semidirect
10. #14271295C2semidirect
11. #14271275C2semidirect
12. #14271237C2semidirect
13. #14271164C2semidirect
14. #102×D29C2semidirect
15. C29×#449C2semidirect
19. C2×SD16×C29C22semidirect
21. C29×#121C22semidirect
29. D4×Dic29C22semidirect
35. C2×C4⋊Dic29C22semidirect
36. C2×#90777C22semidirect
39. #11745250C22semidirect
42. C29×#103C22semidirect
44. C29×C22⋊C8C22semidirect
45. #11745183C22semidirect
46. #11745183C22semidirect
49. #11745180C22semidirect
53. #11745165C22semidirect
54. #11745165C22semidirect
55. #11745163C22semidirect
56. #11745162C22semidirect
58. #11745156C22semidirect
127. D4×C29#41semidirect
196. #449D29semidirect
213. C2×SD16C2×D29semidirect
228. #121C2×D29semidirect
242. #103C2×D29semidirect
251. C22⋊C8C2×D29semidirect
253. C29#3306semidirect
329. D4#90807semidirect

Maximal subgroups

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

subgroupindex
#142718132
#142718012
#142715242
#142714922
#142714822
#142714512
#142714142
#142713892
#142713802
#142712952
#142712752
#142712372
#142711642
#102×D292
C29×#4492
#330629