Finite Group Databasebeta

← D29×#508 #16832606

Subgroups — D29×#508 #16832606

Order 3712.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#135×D29C212yesmaximal, complemented
2#14271596C211yesmaximal, characteristic, complemented
3#14271595C211yesmaximal, characteristic, complemented
4#14271594C212yesmaximal, complemented
5#14271593C212yesmaximal, complemented
6#14271592C211yesmaximal, characteristic, complemented
7Q32×D29C211yesmaximal, characteristic, complemented
8SD32×D29C212yesmaximal, complemented
9D16×D29C211yesmaximal, characteristic, complemented
10C2×C16×D29C211yesmaximal, characteristic, complemented
11C29×#508C211yesmaximal, characteristic, complemented
12#41×D29—22no—
13C29×#135C2212yescomplemented
14#11745312—22no—
15#11745281C2212yescomplemented
16Q16×D29C2212yes—
17#11745278—22no—
18SD16×D29—22no—
19#11745274C2212yescomplemented
20D8×D29C2212yes—
21#11745266C2212yescomplemented
22C2×C8×D29C2211yescharacteristic
23C29×Q32C2211yescharacteristic, complemented
24C29×SD32C2212yescomplemented
25C29×D16C2211yescharacteristic, complemented
26C2×C16×C29C2211yescharacteristic, complemented
27#11745177C2212yescomplemented
28#11745176C2212yescomplemented
29#11745175C2212yescomplemented
30#11745174C2212yescomplemented
31C2×#90768C2211yescharacteristic, complemented
32Dic232C2211yescharacteristic, complemented
33#11745148C2212yescomplemented
34D464C2211yescharacteristic, complemented
35C16×D29C2211yescharacteristic
36C16×D29C2211yescharacteristic
37C16×D29C2211yescharacteristic, complemented
38C16×D29C2211yescharacteristic, complemented
39#41×C29—22no—
40#90809—22no—
41Q8×D29—22no—
42#90807—22no—
43#90807—42no—
44D4×D29—22no—
45D4×D29—42no—
46#90805—22no—
47#90805—42no—
48C2×C4×D29—42no—
49C2×C4×D29D411yescharacteristic
50Q16×C29C2312yes—
51SD16×C29—22no—
52D8×C29C2312yes—
53C2×C8×C29C2311yescharacteristic
54#90785—22no—
55#90784—22no—
56#90783—22no—
57#90782—22no—
58C2×#6597D411yescharacteristic
59Dic116C2312yes—
60D232C2312yes—
61#90773—22no—
62C8×D29D411yescharacteristic
63C8×D29D411yescharacteristic
64C8×D29C2311yescharacteristic
65C8×D29C2311yescharacteristic
66C16×C29C2311yescharacteristic
67C16×C29C2311yescharacteristic
68#90768C2311yescharacteristic
69#90768C2311yescharacteristic
70C22×D29—42no—
71C22×D29D811yescharacteristic
72Q8×C29—22no—
73D4×C29—22no—
74D4×C29—42no—
75C2×C4×C29—42no—
76C2×C4×C29C2×D411yescharacteristic
77C22⋊D29—42no—
78C22⋊D29—42no—
79C22⋊D29—42no—
80C2×Dic29—42no—
81C2×Dic29D811yescharacteristic
82D116—22no—
83D116—42no—
84C4×D29—42no—
85C4×D29—42no—
86C4×D29—42no—
87C4×D29D811yescharacteristic
88C4×D29D811yescharacteristic
89C4×D29C2×D411yescharacteristic
90C4×D29C2×D411yescharacteristic
91Dic58—22no—
92Dic58—42no—
93C8×C29C2×D411yescharacteristic
94C8×C29C2411yescharacteristic
95#6597C2×D411yescharacteristic
96#6597C2×D411yescharacteristic
97C2×#508—291nomaximal, Sylow
98C22×C29—42no—
99C22×C29C2×D811yescharacteristic
100C2×D29—22no—
101C2×D29—42no—
102C2×D29—84no—
103C2×D29C2×D811yescharacteristic
104C2×D29C2×D811yescharacteristic
105C4×C29—42no—
106C4×C29C2×D811yescharacteristic
107C4×C29C22×D411yescharacteristic
108Dic29—42no—
109Dic29C2×D811yescharacteristic
110Dic29C2×D811yescharacteristic
111C2×#135—292no—
112#508—292no—
113#508—291no—
114#508—292no—
115#508—291no—
116#508—291no—
117#508D2911yescharacteristic, direct product factor
118C2×Q32—291no—
119C2×SD32—292no—
120C2×D16—291no—
121C22×C16—291no—
122C2×C29—21no—
123C2×C29—82no—
124C2×C29C22×D811yescharacteristic
125D29—21no—
126D29—82no—
127D29#50812yesdirect product factor
128C2×#41—582no—
129#135—292no—
130#135—292no—
131#135—292no—
132#135—582no—
133#135—582no—
134#135C2×D2912yescomplemented
135C2×Q16—292no—
136C2×SD16—582no—
137C2×D8—292no—
138C22×C8—291no—
139Q32—292no—
140Q32—291no—
141Q32C2×D2911yescharacteristic, complemented
142SD32—292no—
143SD32—292no—
144SD32—292no—
145SD32C2×D2912yescomplemented
146D16—292no—
147D16—291no—
148D16C2×D2911yescharacteristic, complemented
149C2×C16—291no—
150C2×C16—291no—
151C2×C16—291no—
152C2×C16—291no—
153C2×C16—291no—
154C2×C16C2×D2911yescharacteristic, complemented
155C29C2×#50811yescharacteristic, complemented, Sylow
156#41—22no—
157#41—582no—
158#41—582no—
159#41—582no—
160#41—1162no—
161#41—1162no—
162C2×Q8—582no—
163C2×D4—582no—
164C2×D4—1162no—
165C22×C4—291no—
166C22×C4—1162no—
167Q16—292no—
168Q16—582no—
169Q16C22×D2912yes—
170SD16—22no—
171SD16—582no—
172SD16—582no—
173SD16—582no—
174D8—292no—
175D8—582no—
176D8C22×D2912yes—
177C2×C8—291no—
178C2×C8—291no—
179C2×C8—291no—
180C2×C8—291no—
181C2×C8—291no—
182C2×C8C22×D2911yescharacteristic
183C16—291no—
184C16—291no—
185C16C22×D2911yescharacteristic
186C16C22×D2911yescharacteristic
187C23—291no—
188C23—1162no—
189Q8—22no—
190Q8—582no—
191Q8—1162no—
192D4—22no—
193D4—42no—
194D4—582no—
195D4—1162no—
196D4—1162no—
197D4—1162no—
198D4—1162no—
199C2×C4—42no—
200C2×C4—291no—
201C2×C4—291no—
202C2×C4—291no—
203C2×C4—291no—
204C2×C4—291no—
205C2×C4—1162no—
206C2×C4—1162no—
207C2×C4—1162no—
208C2×C4—1162no—
209C2×C4D4×D2911yescharacteristic
210C8—291no—
211C8—291no—
212C8D4×D2911yescharacteristic
213C8C23×D2911yescharacteristic
214C22—42no—
215C22—291no—
216C22—291no—
217C22—582no—
218C22—1162no—
219C22—2324no—
220C22D8×D2911yescharacteristic
221C4—42no—
222C4—291no—
223C4—291no—
224C4—1162no—
225C4D8×D2911yescharacteristic
226C4C2×D4×D2911yescharacteristic
227C2—21no—
228C2—82no—
229C2—292no—
230C2—581no—
231C2—2322no—
232C2C2×D8×D2911yescharacteristic
subgroupG/H
centerC4D8×D29
commutator, cosocleC8×C29C24
FrattiniC8C23×D29
FittingC29×#508C2
socleC2×C29C22×D8
hypercenter#508D29
hypocenterC29C2×#508
LCSG ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D29C2semidirect
2. #14271596C2semidirect
3. #14271595C2semidirect
4. #14271594C2semidirect
5. #14271593C2semidirect
6. #14271592C2semidirect
7. Q32×D29C2semidirect
8. SD32×D29C2semidirect
9. D16×D29C2semidirect
10. C2×C16×D29C2semidirect
11. C29×#508C2semidirect
13. C29×#135C22semidirect
15. #11745281C22semidirect
19. #11745274C22semidirect
21. #11745266C22semidirect
23. C29×Q32C22semidirect
24. C29×SD32C22semidirect
25. C29×D16C22semidirect
26. C2×C16×C29C22semidirect
27. #11745177C22semidirect
28. #11745176C22semidirect
29. #11745175C22semidirect
30. #11745174C22semidirect
31. C2×#90768C22semidirect
32. Dic232C22semidirect
33. #11745148C22semidirect
34. D464C22semidirect
37. C16×D29C22semidirect
38. C16×D29C22semidirect
117. #508D29direct (N × H)
127. D29#508direct (N × H)
134. #135C2×D29semidirect
141. Q32C2×D29semidirect
145. SD32C2×D29semidirect
148. D16C2×D29semidirect
154. C2×C16C2×D29semidirect
155. C29C2×#508semidirect

Maximal subgroups

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

subgroupindex
#135×D292
#142715962
#142715952
#142715942
#142715932
#142715922
Q32×D292
SD32×D292
D16×D292
C2×C16×D292
C29×#5082
C2×#50829