Finite Group Databasebeta

← #16831453

Subgroups — #16831453

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#14271817C211yesmaximal, characteristic, complemented
2#14271522C211yesmaximal, characteristic, complemented
3#14271491C211yesmaximal, characteristic, complemented
4#14271479C211yesmaximal, characteristic, complemented
5#14271453C211yesmaximal, characteristic, complemented
6#14271414C211yesmaximal, characteristic, complemented
7#14271394C211yesmaximal, characteristic, complemented
8#14271375C211yesmaximal, characteristic, complemented
9#14271308C211yesmaximal, characteristic, complemented
10#14271297C211yesmaximal, characteristic, complemented
11#14271273C211yesmaximal, characteristic, complemented
12#14271235C211yesmaximal, characteristic, complemented
13#14271164C211yesmaximal, characteristic, complemented
14C2×#11745180C211yesmaximal, characteristic, complemented
15C29×#546C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×D4×C29C2211yescharacteristic
18C2×#90807—21no—
19C29×#124C2211yescharacteristic
20C29×#123—21no—
21C29×C22⋊Q8C2211yescharacteristic
22C29×#121—21no—
23C29×#121C2211yescharacteristic
24C29×#120—21no—
25C4×D4×C29C2211yescharacteristic
26C4×D4×C29C2211yescharacteristic
27C2×C22⋊C4×C29—21no—
28C2×#90784C2211yescharacteristic, complemented
29C2×#90782C2211yescharacteristic
30C2×#90782C2211yescharacteristic
31#11745292C2211yescharacteristic
32#11745292C2211yescharacteristic, complemented
33C2×C4⋊Dic29C2211yescharacteristic
34C2×C4⋊Dic29C2211yescharacteristic, complemented
35C2×#90777C2211yescharacteristic, complemented
36C22×#6597C2211yescharacteristic
37#11745259—21no—
38#11745248—21no—
39#11745248—21no—
40C4×D116C2211yescharacteristic, complemented
41#11745231C2211yescharacteristic, complemented
42#11745183C2211yescharacteristic, complemented
43#11745183C2211yescharacteristic, complemented
44#11745183C2211yescharacteristic, complemented
45#11745180C2211yescharacteristic
46#11745180C2211yescharacteristic
47#11745180C2211yescharacteristic
48#11745180C2211yescharacteristic
49#11745180C2211yescharacteristic
50#11745180C2211yescharacteristic
51C22⋊#6597C2211yescharacteristic
52C22⋊#6597C2211yescharacteristic, complemented
53#11745157C2211yescharacteristic, complemented
54#11745156C2211yescharacteristic, complemented
55#11745156C2211yescharacteristic, complemented
56#11745156C2211yescharacteristic, complemented
57C4⋊#6597C2211yescharacteristic, complemented
58#11745151C2211yescharacteristic, complemented
59C24×C29—21no—
60#41×C29—22no—
61#41×C29—41no—
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—22no—
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29—41no—
68C2×D4×C29D411yescharacteristic
69C2×D4×C29C2311yescharacteristic
70C2×D4×C29C2311yescharacteristic
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29C2311yescharacteristic
74C22×C4×C29C2311yescharacteristic
75C2×C22⋊D29—21no—
76C2×C22⋊D29—21no—
77C22×Dic29—21no—
78C22×Dic29—21no—
79#90807—44no—
80C2×D116C2311yescharacteristic
81C2×C4×D29—21no—
82C2×Dic58—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29D411yescharacteristic
85C4⋊C4×C29C2311yescharacteristic
86C22⋊C4×C29—21no—
87C22⋊C4×C29—21no—
88C22⋊C4×C29—21no—
89C22⋊C4×C29—21no—
90C22⋊C4×C29—21no—
91C22⋊C4×C29D411yescharacteristic
92C22⋊C4×C29D411yescharacteristic
93C42×C29C2311yescharacteristic
94#90784—41no—
95#90782—22no—
96#90782—41no—
97#90781—21no—
98#90781—21no—
99#90781—21no—
100C4⋊Dic29—21no—
101C4⋊Dic29—21no—
102C4⋊Dic29—21no—
103C4⋊Dic29C2311yescharacteristic
104C4⋊Dic29C2311yescharacteristic
105C4⋊Dic29C2311yescharacteristic
106#90777—41no—
107C2×#6597—41no—
108C2×#6597C2311yescharacteristic
109C2×#6597C2311yescharacteristic
110C2×#6597C2311yescharacteristic
111C2×#6597C2311yescharacteristic
112C23×C29—21no—
113C23×C29—21no—
114C23×C29—42no—
115C23×C29—42no—
116C23×C29—81no—
117C23×C29C2×D411yescharacteristic
118C23×C29C2×D411yescharacteristic
119C22×D29—21no—
120Q8×C29—21no—
121Q8×C29—21no—
122D4×C29—22no—
123D4×C29—21no—
124D4×C29—21no—
125D4×C29—21no—
126D4×C29—42no—
127D4×C29—42no—
128D4×C29—81no—
129D4×C29#4112yescomplemented
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—42no—
137C2×C4×C29—81no—
138C2×C4×C29C2×D411yescharacteristic
139C2×C4×C29C2×D411yescharacteristic
140C2×C4×C29C2×D411yescharacteristic
141C2×C4×C29C2×D411yescharacteristic
142C2×C4×C29C2411yescharacteristic
143C22⋊D29—42no—
144C22⋊D29—42no—
145C2×Dic29—21no—
146C2×Dic29—21no—
147C2×Dic29—21no—
148C2×Dic29—42no—
149C2×Dic29—42no—
150D116—21no—
151D116—21no—
152C4×D29—42no—
153Dic58—42no—
154#6597—21no—
155#6597—21no—
156#6597—21no—
157#6597—21no—
158#3306—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—84no—
171C22×C29AGL(1,ℤ/8)12yes—
172C22×C29C22×D411yescharacteristic
173C2×D29—41no—
174C2×D29—41no—
175C2×D29—41no—
176C4×C29—21no—
177C4×C29—21no—
178C4×C29—21no—
179C4×C29—21no—
180C4×C29—41no—
181C4×C29—41no—
182C4×C29C2×#4111yescharacteristic
183C4×C29H(5,𝔽2)11yescharacteristic
184Dic29—41no—
185Dic29—41no—
186Dic29—41no—
187#547—291no—
188#546D2911yescharacteristic, complemented
189#489—291no—
190#483—291no—
191#481—291no—
192#476—291no—
193#469—291no—
194#465—291no—
195#463—291no—
196#449—291no—
197#447—291no—
198#442—291no—
199#435—291no—
200#417—291no—
201C2×#102—291no—
202C2×C29—22no—
203C2×C29—41no—
204C2×C29—42no—
205C2×C29—81no—
206C2×C29#54611yescharacteristic
207C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
208C2×C29#57711yescharacteristic
209D29—81no—
210C2×#41—581no—
211C2×#41C2×D2911yescharacteristic
212C22×D4C2×D2911yescharacteristic
213C2×SD16—291no—
214C2×D8—291no—
215C2×D8—291no—
216C2×M16—291no—
217C22×C8—291no—
218C4⋊Q8—291no—
219#124C2×D2911yescharacteristic
220#123—21no—
221#123—581no—
222#123—581no—
223C22⋊Q8—581no—
224C22⋊Q8C2×D2911yescharacteristic
225#121—21no—
226#121—291no—
227#121—291no—
228#121C2×D2911yescharacteristic
229#120—21no—
230C4×D4—291no—
231C4×D4C2×D2911yescharacteristic
232C4×D4C2×D2911yescharacteristic
233C2×C4⋊C4—291no—
234C2×C4⋊C4—291no—
235C2×C22⋊C4—21no—
236#106—291no—
237#106—291no—
238#106—291no—
239C4⋊C8—291no—
240#103—291no—
241#103—291no—
242#103—291no—
243#102—291no—
244#102—291no—
245#102—291no—
246#102—291no—
247#102—291no—
248#102—291no—
249#102—291no—
250C22⋊C8—291no—
251C22⋊C8—291no—
252#97—291no—
253C29#330611yescharacteristic, complemented, Sylow
254C24—21no—
255#41—22no—
256#41—41no—
257#41—1164no—
258C2×Q8—581no—
259C2×Q8C22×D2911yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—291no—
266C2×D4—581no—
267C2×D4—581no—
268C2×D4C22⋊D2911yescharacteristic
269C2×D4C22×D2911yescharacteristic
270C2×D4C22×D2911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—581no—
274C22×C4—581no—
275C22×C4—581no—
276C22×C4C22×D2911yescharacteristic
277C22×C4C22×D2911yescharacteristic
278SD16—1161no—
279D8—582no—
280D8—1161no—
281M16—1161no—
282C2×C8—291no—
283C2×C8—291no—
284C2×C8—291no—
285C2×C8—291no—
286C2×C8—1161no—
287C4⋊C4—21no—
288C4⋊C4—291no—
289C4⋊C4—291no—
290C4⋊C4—291no—
291C4⋊C4—581no—
292C4⋊C4—581no—
293C4⋊C4—581no—
294C4⋊C4C22⋊D2911yescharacteristic
295C4⋊C4C22×D2911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—581no—
302C22⋊C4—581no—
303C22⋊C4—581no—
304C22⋊C4C22⋊D2911yescharacteristic
305C22⋊C4C22⋊D2911yescharacteristic
306C42C22×D2911yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—581no—
313C23C2×C22⋊D2911yescharacteristic
314C23C2×C22⋊D2911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1162no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—581no—
326D4—581no—
327D4—1162no—
328D4—1162no—
329D4#9080712yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—581no—
339C2×C4—581no—
340C2×C4—581no—
341C2×C4—1162no—
342C2×C4—1162no—
343C2×C4—1162no—
344C2×C4C2×C22⋊D2911yescharacteristic
345C2×C4C2×C22⋊D2911yescharacteristic
346C2×C4C2×C22⋊D2911yescharacteristic
347C2×C4C2×C22⋊D2911yescharacteristic
348C2×C4C23×D2911yescharacteristic
349C8—581no—
350C8—581no—
351C8—581no—
352C8—581no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—1161no—
366C22—1161no—
367C22—1161no—
368C22#1174531112yes—
369C22C22×C22⋊D2911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—1161no—
377C4—1161no—
378C4—1161no—
379C4C2×#9080711yescharacteristic
380C4#1174535911yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—2321no—
386C2#1427180711yescharacteristic
387C2C2×#1174531111yescharacteristic
388C2#1427197411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#546C2
socleC22×C29C22×D4
hypercenter#546D29
hypocenterC29#3306
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14271817C2semidirect
2. #14271522C2semidirect
3. #14271491C2semidirect
4. #14271479C2semidirect
5. #14271453C2semidirect
6. #14271414C2semidirect
7. #14271394C2semidirect
8. #14271375C2semidirect
9. #14271308C2semidirect
10. #14271297C2semidirect
11. #14271273C2semidirect
12. #14271235C2semidirect
13. #14271164C2semidirect
14. C2×#11745180C2semidirect
15. C29×#546C2semidirect
28. C2×#90784C22semidirect
32. #11745292C22semidirect
34. C2×C4⋊Dic29C22semidirect
35. C2×#90777C22semidirect
40. C4×D116C22semidirect
41. #11745231C22semidirect
42. #11745183C22semidirect
43. #11745183C22semidirect
44. #11745183C22semidirect
52. C22⋊#6597C22semidirect
53. #11745157C22semidirect
54. #11745156C22semidirect
55. #11745156C22semidirect
56. #11745156C22semidirect
57. C4⋊#6597C22semidirect
58. #11745151C22semidirect
129. D4×C29#41semidirect
188. #546D29semidirect
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
#142718172
#142715222
#142714912
#142714792
#142714532
#142714142
#142713942
#142713752
#142713082
#142712972
#142712732
#142712352
#142711642
C2×#117451802
C29×#5462
#330629