Finite Group Databasebeta

← #16831513

Subgroups — #16831513

Order 3712.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14271853C211yesmaximal, characteristic, complemented
2#14271527C211yesmaximal, characteristic, complemented
3#14271484C211yesmaximal, characteristic, complemented
4#14271474C211yesmaximal, characteristic, complemented
5#14271463C211yesmaximal, characteristic, complemented
6#14271407C211yesmaximal, characteristic, complemented
7#14271390C211yesmaximal, characteristic, complemented
8#14271360C211yesmaximal, characteristic, complemented
9#14271314C211yesmaximal, characteristic, complemented
10#14271314C211yesmaximal, characteristic, complemented
11#14271263C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271168C211yesmaximal, characteristic, complemented
14C2×#11745180C211yesmaximal, characteristic, complemented
15D42×C29C211yesmaximal, characteristic
16C22×D4×C29—21no—
17C22×D4×C29C2211yescharacteristic
18C22×D4×C29C2211yescharacteristic
19C29×#127C2211yescharacteristic
20C29×#121—21no—
21C29×#121C2211yescharacteristic
22C29×#121C2211yescharacteristic
23C29×#120—21no—
24C29×#120—21no—
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic
27#11745297—21no—
28C2×#90783C2211yescharacteristic
29C2×#90783C2211yescharacteristic, complemented
30C2×#90783C2211yescharacteristic, complemented
31#11745288C2211yescharacteristic, complemented
32C2×C4⋊Dic29C2211yescharacteristic, complemented
33#11745286C2211yescharacteristic, complemented
34#11745286C2211yescharacteristic, complemented
35C2×#90777C2211yescharacteristic, complemented
36C22×#6597C2211yescharacteristic, complemented
37#11745251—21no—
38#11745241—21no—
39#11745239—21no—
40#11745232C2211yescharacteristic, complemented
41C4×Dic58C2211yescharacteristic, complemented
42#11745180C2211yescharacteristic
43#11745180C2211yescharacteristic
44#11745180C2211yescharacteristic
45#11745180C2211yescharacteristic, complemented
46#11745180C2211yescharacteristic, complemented
47#11745180C2211yescharacteristic, complemented
48#11745180C2211yescharacteristic, complemented
49#11745180C2211yescharacteristic, complemented
50#11745180C2211yescharacteristic, complemented
51C22⋊#6597C2211yescharacteristic, complemented
52C22⋊#6597C2211yescharacteristic, complemented
53#11745158C2211yescharacteristic, complemented
54#11745156C2211yescharacteristic, complemented
55#11745155C2211yescharacteristic, complemented
56#11745155C2211yescharacteristic, complemented
57C4⋊#6597C2211yescharacteristic, complemented
58#11745151C2211yescharacteristic, complemented
59C24×C29—21no—
60C24×C29—21no—
61C2×D4×C29—22no—
62C2×D4×C29—22no—
63C2×D4×C29—21no—
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29—41no—
70C2×D4×C29—41no—
71C2×D4×C29—44no—
72C2×D4×C29D411yescharacteristic
73C2×D4×C29C2311yescharacteristic
74C2×D4×C29C2311yescharacteristic
75C2×D4×C29C2311yescharacteristic
76C22×C4×C29—21no—
77C22×C4×C29C2311yescharacteristic
78C22×C4×C29C2311yescharacteristic
79C22×Dic29—21no—
80C2×Dic58C2311yescharacteristic
81C4⋊C4×C29D411yescharacteristic
82C4⋊C4×C29C2311yescharacteristic
83C22⋊C4×C29—21no—
84C22⋊C4×C29—21no—
85C22⋊C4×C29—21no—
86C22⋊C4×C29D411yescharacteristic
87C22⋊C4×C29D411yescharacteristic
88C42×C29C2311yescharacteristic
89C22⋊Dic29—21no—
90C22⋊Dic29—21no—
91C22⋊Dic29—21no—
92#90783—22no—
93#90783—41no—
94#90783—41no—
95C4⋊Dic29—21no—
96C4⋊Dic29C2311yescharacteristic
97C4⋊Dic29C2311yescharacteristic
98C4⋊Dic29C2311yescharacteristic
99#90779—21no—
100#90779—21no—
101#90779—21no—
102#90779—21no—
103#90779—21no—
104C4×Dic29—21no—
105C4×Dic29—21no—
106#90777—41no—
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C2×#6597C2311yescharacteristic
112C23×C29—21no—
113C23×C29—21no—
114C23×C29—21no—
115C23×C29—42no—
116C23×C29—42no—
117C23×C29—42no—
118C23×C29—42no—
119C23×C29—81no—
120C23×C29—81no—
121C23×C29C2×D411yescharacteristic
122C23×C29C2×D411yescharacteristic
123D4×C29—22no—
124D4×C29—21no—
125D4×C29—21no—
126D4×C29—21no—
127D4×C29—21no—
128D4×C29—21no—
129D4×C29—42no—
130D4×C29—42no—
131D4×C29—42no—
132D4×C29—42no—
133D4×C29—42no—
134D4×C29—81no—
135D4×C29#4112yes—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—42no—
142C2×C4×C29C2×D411yescharacteristic
143C2×C4×C29C2×D411yescharacteristic
144C2×C4×C29C2×D411yescharacteristic
145C2×C4×C29C2×D411yescharacteristic
146C2×C4×C29C2411yescharacteristic
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29—21no—
150C2×Dic29—21no—
151C2×Dic29—42no—
152Dic58—21no—
153Dic58—21no—
154#6597—21no—
155#6597—21no—
156#6597—21no—
157#6597—21no—
158#3310—291nomaximal, Sylow
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—22no—
163C22×C29—21no—
164C22×C29—21no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29—41no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29—41no—
172C22×C29—41no—
173C22×C29—84no—
174C22×C29—84no—
175C22×C29AGL(1,ℤ/8)12yes—
176C22×C29C22×D411yescharacteristic
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—21no—
181C4×C29—41no—
182C4×C29C2×#4111yescharacteristic
183C4×C29H(5,𝔽2)11yescharacteristic
184Dic29—41no—
185Dic29—41no—
186Dic29—41no—
187Dic29—41no—
188#552—291no—
189D42D2911yescharacteristic
190#490—291no—
191#482—291no—
192#480—291no—
193#478—291no—
194#468—291no—
195#465—291no—
196#460—291no—
197#450—291no—
198#450—291no—
199#440—291no—
200#435—291no—
201#418—291no—
202C2×#102—291no—
203C2×C29—22no—
204C2×C29—41no—
205C2×C29—42no—
206C2×C29—81no—
207C2×C29—81no—
208C2×C29#54611yescharacteristic
209C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
210C2×C29#57711yescharacteristic
211C22×D4—21no—
212C22×D4C2×D2911yescharacteristic
213C22×D4C2×D2911yescharacteristic
214C2×SD16—291no—
215C2×SD16—291no—
216C2×SD16—291no—
217C2×M16—291no—
218C22×C8—291no—
219#127C2×D2911yescharacteristic
220#126—581no—
221#125—291no—
222#125—581no—
223#123—581no—
224C22⋊Q8—291no—
225C22⋊Q8—291no—
226#121—21no—
227#121C2×D2911yescharacteristic
228#121C2×D2911yescharacteristic
229#120—21no—
230#120—21no—
231C4×Q8—291no—
232C4×D4C2×D2911yescharacteristic
233C4×D4C2×D2911yescharacteristic
234#117—291no—
235#117—581no—
236C2×C4⋊C4—291no—
237#107—291no—
238#107—291no—
239#106—291no—
240C4⋊C8—291no—
241#103—291no—
242#102—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250#102—291no—
251C22⋊C8—291no—
252C22⋊C8—291no—
253#97—291no—
254C29#331011yescharacteristic, complemented, Sylow
255C24—21no—
256C24—21no—
257C2×Q8—291no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D2911yescharacteristic
270C2×D4C22×D2911yescharacteristic
271C2×D4C22×D2911yescharacteristic
272C2×D4C22×D2911yescharacteristic
273C22×C4—21no—
274C22×C4—581no—
275C22×C4C22×D2911yescharacteristic
276C22×C4C22×D2911yescharacteristic
277SD16—582no—
278SD16—1161no—
279SD16—1161no—
280M16—1161no—
281C2×C8—291no—
282C2×C8—291no—
283C2×C8—291no—
284C2×C8—291no—
285C2×C8—1161no—
286C4⋊C4—291no—
287C4⋊C4—291no—
288C4⋊C4—291no—
289C4⋊C4—581no—
290C4⋊C4—581no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4—581no—
295C4⋊C4C22⋊D2911yescharacteristic
296C4⋊C4C22×D2911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—581no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4C22⋊D2911yescharacteristic
304C22⋊C4C22⋊D2911yescharacteristic
305C42—581no—
306C42—581no—
307C42C22×D2911yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D2911yescharacteristic
318C23C2×C22⋊D2911yescharacteristic
319Q8—581no—
320Q8—581no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#9080712yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—581no—
341C2×C4—581no—
342C2×C4—581no—
343C2×C4—581no—
344C2×C4—1162no—
345C2×C4C2×C22⋊D2911yescharacteristic
346C2×C4C2×C22⋊D2911yescharacteristic
347C2×C4C2×C22⋊D2911yescharacteristic
348C2×C4C2×C22⋊D2911yescharacteristic
349C2×C4C23×D2911yescharacteristic
350C8—581no—
351C8—581no—
352C8—581no—
353C8—581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1174529412yes—
371C22C22×C22⋊D2911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—1161no—
378C4—1161no—
379C4—1161no—
380C4—1161no—
381C4C2×#9080711yescharacteristic
382C4#1174535911yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1427180711yescharacteristic
389C2C2×#1174529411yescharacteristic
390C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
Fitting, prime radicalD42×C29C2
socleC22×C29C22×D4
hypercenterD42D29
hypocenterC29#3310
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14271853C2semidirect
2. #14271527C2semidirect
3. #14271484C2semidirect
4. #14271474C2semidirect
5. #14271463C2semidirect
6. #14271407C2semidirect
7. #14271390C2semidirect
8. #14271360C2semidirect
9. #14271314C2semidirect
10. #14271314C2semidirect
11. #14271263C2semidirect
12. #14271235C2semidirect
13. #14271168C2semidirect
14. C2×#11745180C2semidirect
29. C2×#90783C22semidirect
30. C2×#90783C22semidirect
31. #11745288C22semidirect
32. C2×C4⋊Dic29C22semidirect
33. #11745286C22semidirect
34. #11745286C22semidirect
35. C2×#90777C22semidirect
36. C22×#6597C22semidirect
40. #11745232C22semidirect
41. C4×Dic58C22semidirect
45. #11745180C22semidirect
46. #11745180C22semidirect
47. #11745180C22semidirect
48. #11745180C22semidirect
49. #11745180C22semidirect
50. #11745180C22semidirect
51. C22⋊#6597C22semidirect
52. C22⋊#6597C22semidirect
53. #11745158C22semidirect
54. #11745156C22semidirect
55. #11745155C22semidirect
56. #11745155C22semidirect
57. C4⋊#6597C22semidirect
58. #11745151C22semidirect
254. C29#3310semidirect

Maximal subgroups

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

subgroupindex
#142718532
#142715272
#142714842
#142714742
#142714632
#142714072
#142713902
#142713602
#142713142
#142712632
#142712352
#142711682
C2×#117451802
D42×C292
#331029