Finite Group Databasebeta

← #16831309

Subgroups — #16831309

Order 3712.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271871C211yesmaximal, characteristic, complemented
2D4×C22⋊D29C211yesmaximal, characteristic
3#14271508C211yesmaximal, characteristic, complemented
4#14271482C211yesmaximal, characteristic, complemented
5#14271480C211yesmaximal, characteristic, complemented
6#14271451C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271389C211yesmaximal, characteristic, complemented
9#14271361C211yesmaximal, characteristic, complemented
10#14271312C211yesmaximal, characteristic, complemented
11SD16×Dic29C211yesmaximal, characteristic, complemented
12#14271226C211yesmaximal, characteristic, complemented
13C2×#11745180C211yesmaximal, characteristic, complemented
14#102×D29C211yesmaximal, characteristic, complemented
15C29×#450C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C22×C22⋊D29—21no—
18C2×D4×D29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic, complemented
21C29×C22⋊Q8C2211yescharacteristic, complemented
22#11745315—21no—
23#11745308C2211yescharacteristic, complemented
24Q8×Dic29C2211yescharacteristic, complemented
25C2×#90784C2211yescharacteristic, complemented
26#11745302C2211yescharacteristic
27#11745301—21no—
28#11745300C2211yescharacteristic
29#11745299—21no—
30D4×Dic29C2211yescharacteristic
31#11745292C2211yescharacteristic
32C4×C22⋊D29C2211yescharacteristic
33C2×C4⋊Dic29C2211yescharacteristic, complemented
34C22×#6597C2211yescharacteristic, complemented
35C2×C8×D29C2211yescharacteristic, complemented
36#11745259—21no—
37C4⋊C4×D29C2211yescharacteristic, complemented
38#11745251—21no—
39#11745250C2211yescharacteristic, complemented
40#11745243—21no—
41#11745240—21no—
42C29×#102C2211yescharacteristic
43C29×#102C2211yescharacteristic, complemented
44C29×C22⋊C8C2211yescharacteristic, complemented
45#11745183C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic, complemented
49#11745180C2211yescharacteristic, complemented
50#11745169C2211yescharacteristic, complemented
51#11745169C2211yescharacteristic, complemented
52#11745168C2211yescharacteristic, complemented
53#11745165C2211yescharacteristic, complemented
54#11745165C2211yescharacteristic, complemented
55#11745162C2211yescharacteristic, complemented
56C8×Dic29C2211yescharacteristic, complemented
57#11745157C2211yescharacteristic, complemented
58#11745156C2211yescharacteristic, complemented
59C24×C29—21no—
60C23×D29—21no—
61C2×Q8×C29C2311yescharacteristic
62C2×D4×C29—22no—
63C2×D4×C29—21no—
64C2×D4×C29—41no—
65C2×D4×C29C2311yescharacteristic
66C2×D4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C2×C22⋊D29—21no—
69C2×C22⋊D29—21no—
70C2×C22⋊D29—21no—
71C2×C22⋊D29—21no—
72C2×C22⋊D29—21no—
73C2×C22⋊D29—44no—
74C2×C22⋊D29D411yescharacteristic
75C22×Dic29—21no—
76C22×Dic29—21no—
77D4×D29—22no—
78D4×D29—41no—
79C2×D116C2311yescharacteristic
80C2×C4×D29—21no—
81C2×C4×D29C2311yescharacteristic
82C2×Dic58—21no—
83SD16×C29—22no—
84SD16×C29—41no—
85C2×C8×C29C2311yescharacteristic
86C2×C8×C29C2311yescharacteristic
87C4⋊C4×C29—21no—
88C4⋊C4×C29C2311yescharacteristic
89C22⋊C4×C29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29—21no—
92C22⋊Dic29D411yescharacteristic
93#90784—41no—
94#90781—21no—
95#90781—21no—
96#90781D411yescharacteristic
97C4⋊Dic29—21no—
98C4⋊Dic29—21no—
99C4⋊Dic29C2311yescharacteristic
100C4⋊Dic29C2311yescharacteristic
101C4⋊Dic29C2311yescharacteristic
102#90779—21no—
103#90779—21no—
104#90779—21no—
105#90779D411yescharacteristic
106C4×Dic29—21no—
107C4×Dic29C2311yescharacteristic
108C2×#6597—41no—
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C8×D29—41no—
112C23×C29—21no—
113C23×C29—21no—
114C23×C29—42no—
115C23×C29—42no—
116C23×C29—81no—
117C23×C29C2×D411yescharacteristic
118C22×D29—21no—
119C22×D29—42no—
120C22×D29—42no—
121C22×D29—81no—
122C22×D29C2×D411yescharacteristic
123Q8×C29—21no—
124Q8×C29—21no—
125D4×C29—21no—
126D4×C29—21no—
127D4×C29—21no—
128D4×C29—42no—
129D4×C29#4112yes—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2411yescharacteristic
136C22⋊D29—42no—
137C22⋊D29—42no—
138C22⋊D29—42no—
139C22⋊D29—42no—
140C22⋊D29—81no—
141C22⋊D29SD1614yescomplemented
142C2×Dic29—21no—
143C2×Dic29—21no—
144C2×Dic29—21no—
145C2×Dic29—42no—
146C2×Dic29—81no—
147C2×Dic29C2×D411yescharacteristic
148C2×Dic29C2×D411yescharacteristic
149C2×Dic29C2×D411yescharacteristic
150D116—21no—
151D116—21no—
152C4×D29—21no—
153C4×D29—21no—
154C4×D29—81no—
155Dic58—81no—
156C8×C29—21no—
157C8×C29—21no—
158#6597—21no—
159#6597—21no—
160#3295—291nomaximal, Sylow
161C22×C29—21no—
162C22×C29—21no—
163C22×C29—22no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29—41no—
169C22×C29—84no—
170C22×C29C2×SD1612yes—
171C22×C29C22×D411yescharacteristic
172C2×D29—21no—
173C2×D29—21no—
174C2×D29—41no—
175C2×D29—41no—
176C2×D29—41no—
177C2×D29—84no—
178C2×D29C2×SD1612yes—
179C4×C29—21no—
180C4×C29—41no—
181C4×C29—41no—
182C4×C29C2×#4111yescharacteristic
183C4×C29H(5,𝔽2)11yescharacteristic
184Dic29—21no—
185Dic29—21no—
186Dic29—41no—
187Dic29—41no—
188Dic29—41no—
189Dic29C2×SD1612yes—
190#554—291no—
191D42—291no—
192#486—291no—
193#481—291no—
194#481—291no—
195#476—291no—
196#465—291no—
197#465—291no—
198#460—291no—
199#450—291no—
200#450D2911yescharacteristic, complemented
201C4×SD16—291no—
202C8×D4—291no—
203C2×#102—291no—
204C2×#102—291no—
205C2×C29—22no—
206C2×C29—42no—
207C2×C29—81no—
208C2×C29#54611yescharacteristic
209C2×C29C22×SD1611yescharacteristic
210C2×C29#57611yescharacteristic
211D29—22no—
212D29—81no—
213C22×D4—291no—
214C22×D4—581no—
215C22×D4C2×D2911yescharacteristic
216C2×SD16—291no—
217C2×SD16C2×D2911yescharacteristic
218C2×SD16C2×D2911yescharacteristic, complemented
219C22×C8—291no—
220C22×C8—291no—
221C4⋊Q8—291no—
222#127—291no—
223#125—581no—
224C22⋊Q8—291no—
225C22⋊Q8—581no—
226C22⋊Q8—581no—
227C22⋊Q8C2×D2911yescharacteristic, complemented
228#121—291no—
229#121—291no—
230#121—581no—
231#120—581no—
232#120—581no—
233C4×Q8—291no—
234C4×D4—291no—
235C4×D4—291no—
236C4×D4—581no—
237C2×C4⋊C4—291no—
238C2×C4⋊C4—291no—
239#106—291no—
240#106—291no—
241#106—291no—
242C4⋊C8—291no—
243#103—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250#102—291no—
251#102C2×D2911yescharacteristic
252#102C2×D2911yescharacteristic, complemented
253C22⋊C8—291no—
254C22⋊C8C2×D2911yescharacteristic, complemented
255C4×C8—291no—
256C29#329511yescharacteristic, complemented, Sylow
257C24—21no—
258C24—581no—
259C2×Q8—581no—
260C2×Q8C22×D2911yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—291no—
265C2×D4—291no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4—581no—
269C2×D4—582no—
270C2×D4—581no—
271C2×D4—581no—
272C2×D4—1161no—
273C2×D4—1164no—
274C2×D4C22×D2911yescharacteristic
275C2×D4C22×D2911yescharacteristic
276C22×C4—291no—
277C22×C4—581no—
278C22×C4—581no—
279C22×C4—581no—
280C22×C4C22×D2911yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—1161no—
284C2×C8—291no—
285C2×C8—291no—
286C2×C8—1161no—
287C2×C8—1161no—
288C2×C8C22×D2911yescharacteristic
289C2×C8C22×D2911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—291no—
292C4⋊C4—291no—
293C4⋊C4—291no—
294C4⋊C4—291no—
295C4⋊C4—581no—
296C4⋊C4—581no—
297C4⋊C4—581no—
298C4⋊C4—581no—
299C4⋊C4—581no—
300C4⋊C4C22×D2911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—291no—
303C22⋊C4—291no—
304C22⋊C4—581no—
305C22⋊C4—581no—
306C22⋊C4—581no—
307C22⋊C4—581no—
308C42—291no—
309C42—581no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—291no—
316C23—581no—
317C23—1162no—
318C23—1162no—
319C23—2321no—
320C23D4×D2911yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—2321no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—294no—
329D4—581no—
330D4—581no—
331D4—1162no—
332D4—1162no—
333D4—1162no—
334D4—1162no—
335D4—2321no—
336D4#9080712yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—291no—
342C2×C4—291no—
343C2×C4—291no—
344C2×C4—581no—
345C2×C4—581no—
346C2×C4—581no—
347C2×C4—581no—
348C2×C4—581no—
349C2×C4—1162no—
350C2×C4—2321no—
351C2×C4—2321no—
352C2×C4D4×D2911yescharacteristic
353C2×C4C23×D2911yescharacteristic
354C8—21no—
355C8—21no—
356C8—581no—
357C8—581no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—292no—
368C22—581no—
369C22—581no—
370C22—1161no—
371C22—1161no—
372C22—1161no—
373C22—2324no—
374C22SD16×D2912yes—
375C22C2×D4×D2911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—292no—
380C4—581no—
381C4—581no—
382C4—1161no—
383C4—1161no—
384C4—1161no—
385C4C2×#9080711yescharacteristic
386C4#1174535911yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—582no—
391C2—2321no—
392C2#1427180011yescharacteristic
393C2C2×SD16×D2911yescharacteristic
394C2#1427196711yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#450C2
socleC22×C29C22×D4
prime radicalD4×C22⋊D29C2
hypercenter#450D29
hypocenterC29#3295
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14271871C2semidirect
3. #14271508C2semidirect
4. #14271482C2semidirect
5. #14271480C2semidirect
6. #14271451C2semidirect
7. #14271394C2semidirect
8. #14271389C2semidirect
9. #14271361C2semidirect
10. #14271312C2semidirect
11. SD16×Dic29C2semidirect
12. #14271226C2semidirect
13. C2×#11745180C2semidirect
14. #102×D29C2semidirect
15. C29×#450C2semidirect
20. C2×SD16×C29C22semidirect
21. C29×C22⋊Q8C22semidirect
23. #11745308C22semidirect
24. Q8×Dic29C22semidirect
25. C2×#90784C22semidirect
33. C2×C4⋊Dic29C22semidirect
34. C22×#6597C22semidirect
35. C2×C8×D29C22semidirect
37. C4⋊C4×D29C22semidirect
39. #11745250C22semidirect
43. C29×#102C22semidirect
44. C29×C22⋊C8C22semidirect
45. #11745183C22semidirect
48. #11745180C22semidirect
49. #11745180C22semidirect
50. #11745169C22semidirect
51. #11745169C22semidirect
52. #11745168C22semidirect
53. #11745165C22semidirect
54. #11745165C22semidirect
55. #11745162C22semidirect
56. C8×Dic29C22semidirect
57. #11745157C22semidirect
58. #11745156C22semidirect
141. C22⋊D29SD16semidirect
200. #450D29semidirect
218. C2×SD16C2×D29semidirect
227. C22⋊Q8C2×D29semidirect
252. #102C2×D29semidirect
254. C22⋊C8C2×D29semidirect
256. C29#3295semidirect

Maximal subgroups

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

subgroupindex
#142718712
D4×C22⋊D292
#142715082
#142714822
#142714802
#142714512
#142713942
#142713892
#142713612
#142713122
SD16×Dic292
#142712262
C2×#117451802
#102×D292
C29×#4502
#329529