Finite Group Databasebeta

← #16832624

Subgroups — #16832624

Order 3712.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745274C211yesmaximal, characteristic, complemented
2#135×D29C211yesmaximal, characteristic, complemented
3#14271606C211yesmaximal, characteristic, complemented
4#14271603C211yesmaximal, characteristic, complemented
5#14271602C212yesmaximal, complemented
6#14271599C211yesmaximal, characteristic, complemented
7#14271597C212yesmaximal, complemented
8#14271594C212yesmaximal, complemented
9#14271592C212yesmaximal, complemented
10M32×D29C211yesmaximal, characteristic, complemented
11C29×#509C211yesmaximal, characteristic, complemented
12#41×D29—21no—
13C2×#90807—21no—
14C29×#135C2211yescharacteristic
15C2×D8×C29C2211yescharacteristic, complemented
16#11745312—21no—
17C2×#90783—21no—
18#11745281C2211yescharacteristic, complemented
19Q16×D29C2211yescharacteristic, complemented
20#11745278—21no—
21SD16×D29—21no—
22#11745274—21no—
23#11745274—21no—
24#11745274C2212yes—
25#11745274C2211yescharacteristic, complemented
26#11745274C2212yescomplemented
27D8×D29C2211yescharacteristic, complemented
28C2×Dic116C2211yescharacteristic, complemented
29#11745266C2211yescharacteristic
30C2×C8×D29C2211yescharacteristic
31C29×SD32C2212yescomplemented
32C29×D16C2212yescomplemented
33C29×M32C2211yescharacteristic, complemented
34#11745177C2212yescomplemented
35#11745175C2212yescomplemented
36#11745175C2212yescomplemented
37#11745174C2212yescomplemented
38#11745160C2211yescharacteristic, complemented
39Dic232C2212yescomplemented
40#11745148C2212yescomplemented
41#11745146C2212yescomplemented
42C16×D29C2212yescomplemented
43#41×C29—21no—
44C2×D4×C29—21no—
45C2×C22⋊D29—41no—
46C22×Dic29—41no—
47#90809—21no—
48Q8×D29—21no—
49#90807—22no—
50#90807—22no—
51#90807—21no—
52#90807—41no—
53#90807—41no—
54#90807—41no—
55D4×D29—21no—
56D4×D29—41no—
57#90805—21no—
58#90805—41no—
59C2×C4×D29—41no—
60C2×C4×D29D411yescharacteristic
61C2×Dic58—21no—
62Q16×C29C2311yescharacteristic
63SD16×C29—21no—
64D8×C29—21no—
65D8×C29C2312yes—
66D8×C29C2311yescharacteristic
67C2×C8×C29C2311yescharacteristic
68#90785—21no—
69#90784—21no—
70#90783—22no—
71#90783—22no—
72#90783—21no—
73#90782—21no—
74C2×#6597D411yescharacteristic
75Dic116—21no—
76Dic116C2312yes—
77Dic116C2311yescharacteristic
78D232C2311yescharacteristic
79#90773—21no—
80C8×D29D411yescharacteristic
81C8×D29D411yescharacteristic
82C8×D29C2311yescharacteristic
83C8×D29C2311yescharacteristic
84C16×C29C2312yes—
85#90768C2312yes—
86C23×C29—41no—
87C22×D29—41no—
88C22×D29D811yescharacteristic
89Q8×C29—21no—
90D4×C29—21no—
91D4×C29—22no—
92D4×C29—41no—
93D4×C29—41no—
94C2×C4×C29—41no—
95C2×C4×C29C2×D411yescharacteristic
96C22⋊D29—41no—
97C22⋊D29—41no—
98C22⋊D29—42no—
99C22⋊D29—42no—
100C22⋊D29—41no—
101C2×Dic29—41no—
102C2×Dic29—41no—
103C2×Dic29—42no—
104C2×Dic29—42no—
105C2×Dic29D811yescharacteristic
106D116—21no—
107D116—41no—
108C4×D29—41no—
109C4×D29—41no—
110C4×D29—41no—
111C4×D29D811yescharacteristic
112C4×D29D811yescharacteristic
113C4×D29C2×D411yescharacteristic
114C4×D29C2×D411yescharacteristic
115Dic58—21no—
116Dic58—22no—
117Dic58—41no—
118Dic58—41no—
119C8×C29C2×D411yescharacteristic
120C8×C29C2411yescharacteristic
121#6597C2×D411yescharacteristic
122#6597C2×D411yescharacteristic
123#3414—291nomaximal, Sylow
124C22×C29—42no—
125C22×C29—41no—
126C22×C29—82no—
127C22×C29C2×D811yescharacteristic
128C2×D29—41no—
129C2×D29—41no—
130C2×D29—82no—
131C2×D29C2×D811yescharacteristic
132C2×D29C2×D811yescharacteristic
133C4×C29—41no—
134C4×C29C2×D811yescharacteristic
135C4×C29C22×D411yescharacteristic
136Dic29—41no—
137Dic29—42no—
138Dic29C2×D811yescharacteristic
139Dic29C2×D811yescharacteristic
140C2×#135—291no—
141C2×#135—291no—
142#510—291no—
143#510—292no—
144#510—291no—
145#509—291no—
146#509—292no—
147#509D2911yescharacteristic, complemented
148#508—292no—
149#508—292no—
150C2×M32—291no—
151C2×C29—21no—
152C2×C29—81no—
153C2×C29—82no—
154C2×C29C22×D811yescharacteristic
155D29—21no—
156D29—21no—
157D29—81no—
158C2×#41—581no—
159C2×#41—581no—
160#135—291no—
161#135—292no—
162#135—292no—
163#135—291no—
164#135—291no—
165#135—581no—
166#135—581no—
167#135—581no—
168#135—581no—
169#135C2×D2911yescharacteristic
170C2×Q16—291no—
171C2×Q16—291no—
172C2×SD16—581no—
173C2×SD16—581no—
174C2×D8—291no—
175C2×D8C2×D2911yescharacteristic, complemented
176C22×C8—291no—
177Q32—292no—
178Q32—292no—
179SD32—292no—
180SD32—292no—
181SD32—292no—
182SD32C2×D2912yescomplemented
183D16—292no—
184D16C2×D2912yescomplemented
185M32—291no—
186M32—292no—
187M32C2×D2911yescharacteristic, complemented
188C2×C16—292no—
189C29#341411yescharacteristic, complemented, Sylow
190#41—21no—
191#41—582no—
192#41—582no—
193#41—581no—
194#41—581no—
195#41—581no—
196#41—1161no—
197#41—1161no—
198#41—1161no—
199#41—1161no—
200C2×Q8—581no—
201C2×Q8—581no—
202C2×D4—21no—
203C2×D4—581no—
204C2×D4—1161no—
205C2×D4—1161no—
206C22×C4—291no—
207C22×C4—1161no—
208C22×C4—1161no—
209Q16—291no—
210Q16—292no—
211Q16—581no—
212Q16—581no—
213Q16C22×D2911yescharacteristic
214SD16—21no—
215SD16—582no—
216SD16—582no—
217SD16—581no—
218SD16—581no—
219SD16—581no—
220D8—21no—
221D8—291no—
222D8—581no—
223D8C22×D2912yes—
224D8C22×D2911yescharacteristic
225C2×C8—291no—
226C2×C8—291no—
227C2×C8—291no—
228C2×C8—291no—
229C2×C8—291no—
230C2×C8C22×D2911yescharacteristic
231C16—292no—
232C16C22×D2912yes—
233C23—41no—
234C23—291no—
235C23—1161no—
236Q8—21no—
237Q8—582no—
238Q8—581no—
239Q8—1161no—
240Q8—1161no—
241D4—22no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—581no—
246D4—1161no—
247D4—1161no—
248D4—1161no—
249D4—1162no—
250D4—1162no—
251D4—1161no—
252C2×C4—41no—
253C2×C4—291no—
254C2×C4—291no—
255C2×C4—291no—
256C2×C4—291no—
257C2×C4—291no—
258C2×C4—1161no—
259C2×C4—1161no—
260C2×C4—1161no—
261C2×C4—1162no—
262C2×C4—1162no—
263C2×C4—1161no—
264C2×C4—1161no—
265C2×C4D4×D2911yescharacteristic
266C8—291no—
267C8—291no—
268C8D4×D2911yescharacteristic
269C8C23×D2911yescharacteristic
270C22—41no—
271C22—42no—
272C22—82no—
273C22—291no—
274C22—291no—
275C22—1161no—
276C22—1161no—
277C22—2322no—
278C22D8×D2911yescharacteristic
279C4—41no—
280C4—291no—
281C4—291no—
282C4—1161no—
283C4—1162no—
284C4D8×D2911yescharacteristic
285C4C2×D4×D2911yescharacteristic
286C2—21no—
287C2—82no—
288C2—81no—
289C2—581no—
290C2—581no—
291C2—2321no—
292C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC2C2×D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC29×#509C2
socleC2×C29C22×D8
hypercenter#509D29
hypocenterC29#3414
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. C2×#11745274C2semidirect
2. #135×D29C2semidirect
3. #14271606C2semidirect
4. #14271603C2semidirect
5. #14271602C2semidirect
6. #14271599C2semidirect
7. #14271597C2semidirect
8. #14271594C2semidirect
9. #14271592C2semidirect
10. M32×D29C2semidirect
11. C29×#509C2semidirect
15. C2×D8×C29C22semidirect
18. #11745281C22semidirect
19. Q16×D29C22semidirect
25. #11745274C22semidirect
26. #11745274C22semidirect
27. D8×D29C22semidirect
28. C2×Dic116C22semidirect
31. C29×SD32C22semidirect
32. C29×D16C22semidirect
33. C29×M32C22semidirect
34. #11745177C22semidirect
35. #11745175C22semidirect
36. #11745175C22semidirect
37. #11745174C22semidirect
38. #11745160C22semidirect
39. Dic232C22semidirect
40. #11745148C22semidirect
41. #11745146C22semidirect
42. C16×D29C22semidirect
147. #509D29semidirect
175. C2×D8C2×D29semidirect
182. SD32C2×D29semidirect
184. D16C2×D29semidirect
187. M32C2×D29semidirect
189. C29#3414semidirect

Maximal subgroups

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

subgroupindex
C2×#117452742
#135×D292
#142716062
#142716032
#142716022
#142715992
#142715972
#142715942
#142715922
M32×D292
C29×#5092
#341429