Finite Group Databasebeta

← D29×#487 #16829800

Subgroups — D29×#487 #16829800

Order 3712.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D29C211yesmaximal, characteristic
2C4⋊Q8×D29C211yesmaximal, characteristic
3#14271515C211yesmaximal, characteristic, complemented
4#14271514C211yesmaximal, characteristic, complemented
5#14271513C211yesmaximal, characteristic, complemented
6#14271512C214yesmaximal, complemented
7#103×D29C214yesmaximal
8C4×C8×D29C211yesmaximal, characteristic
9C29×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D29—21no—
11C2×Q8×D29C2212yes—
12C29×C4⋊Q8C2211yescharacteristic
13C29×C4⋊Q8C2211yescharacteristic
14#11745306—21no—
15#11745306C2212yes—
16C2×C8×D29C2212yes—
17C4⋊C4×D29—21no—
18C4⋊C4×D29—21no—
19C4⋊C4×D29—21no—
20C4⋊C4×D29C2212yes—
21#11745250—21no—
22#11745250—21no—
23#11745250—21no—
24#11745250C2212yes—
25C42×D29C2211yescharacteristic
26#11745231C2211yescharacteristic
27#11745231C2211yescharacteristic
28C29×#103C2214yes—
29C4×C8×C29C2211yescharacteristic
30#11745183C2214yes—
31#11745164C2214yes—
32C8×Dic29C2212yes—
33#11745158C2214yes—
34C4×#6597C2211yescharacteristic
35C2×Q8×C29—21no—
36C2×Q8×C29C2312yes—
37Q8×D29—28no—
38Q8×D29—44no—
39C2×C4×D29—22no—
40C2×C4×D29—22no—
41C2×C4×D29D411yescharacteristic
42C2×C4×D29D411yescharacteristic
43C2×C4×D29C2311yescharacteristic
44C2×Dic58—21no—
45C2×Dic58—22no—
46C2×Dic58—22no—
47C2×Dic58C2312yes—
48C2×C8×C29C2312yes—
49C4⋊C4×C29—21no—
50C4⋊C4×C29—21no—
51C4⋊C4×C29—21no—
52C4⋊C4×C29C2312yes—
53C42×C29C2311yescharacteristic
54C4⋊Dic29—21no—
55C4⋊Dic29—21no—
56C4⋊Dic29—21no—
57C4⋊Dic29C2312yes—
58#90779—22no—
59#90779—22no—
60#90779—22no—
61#90779—22no—
62C4×Dic29D411yescharacteristic
63C4×Dic29D411yescharacteristic
64C4×Dic29C2311yescharacteristic
65C2×#6597C2312yes—
66C8×D29—24no—
67C22×D29C2×D411yescharacteristic
68Q8×C29—24no—
69Q8×C29—42no—
70C2×C4×C29—22no—
71C2×C4×C29—22no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2411yescharacteristic
75C2×Dic29—22no—
76C2×Dic29—22no—
77C2×Dic29C2×D411yescharacteristic
78C2×Dic29C2×D411yescharacteristic
79C2×Dic29C2×D411yescharacteristic
80C4×D29—44no—
81C4×D29—44no—
82C4×D29SD1614yes—
83C4×D29Q1614yes—
84C4×D29#4114yes—
85Dic58—24no—
86Dic58—42no—
87Dic58—44no—
88Dic58—44no—
89C8×C29—22no—
90#6597—22no—
91C2×#487—291nomaximal, Sylow
92C22×C29C22×D411yescharacteristic
93C2×D29#12412yes—
94C2×D29C2×SD1612yes—
95C2×D29C2×Q1612yes—
96C4×C29—42no—
97C4×C29—42no—
98C4×C29C2×SD1612yes—
99C4×C29C2×Q1612yes—
100C4×C29C2×#4112yes—
101Dic29—42no—
102Dic29—42no—
103Dic29#12412yes—
104Dic29C2×SD1612yes—
105Dic29C2×Q1612yes—
106C2×C4⋊Q8—291no—
107C2×C4⋊Q8—291no—
108#487—291no—
109#487—291no—
110#487—294no—
111#487—291no—
112#487D2911yescharacteristic, direct product factor
113C2×#103—294no—
114C2×C4×C8—291no—
115C2×C29C2×#12411yescharacteristic
116C2×C29C22×SD1611yescharacteristic
117C2×C29C22×Q1611yescharacteristic
118D29#48714yesdirect product factor
119C22×Q8—292no—
120C22×Q8—581no—
121C22×C8—292no—
122C4⋊Q8—292no—
123C4⋊Q8—292no—
124C4⋊Q8—291no—
125C4⋊Q8—291no—
126C4⋊Q8—581no—
127C4⋊Q8—581no—
128C4⋊Q8—581no—
129C4⋊Q8—581no—
130C4⋊Q8C2×D2911yescharacteristic
131C4⋊Q8C2×D2911yescharacteristic
132C2×C4⋊C4—292no—
133C2×C4⋊C4—581no—
134C2×C4⋊C4—581no—
135C2×C4⋊C4—581no—
136C2×C42—291no—
137#103—294no—
138#103—294no—
139#103—294no—
140#103C2×D2914yes—
141C4×C8—292no—
142C4×C8—291no—
143C4×C8C2×D2911yescharacteristic
144C29C2×#48711yescharacteristic, complemented, Sylow
145C2×Q8—21no—
146C2×Q8—292no—
147C2×Q8—582no—
148C2×Q8—582no—
149C2×Q8—588no—
150C2×Q8—581no—
151C2×Q8—1164no—
152C2×Q8C22×D2912yes—
153C22×C4—291no—
154C22×C4—291no—
155C22×C4—291no—
156C22×C4—582no—
157C22×C4—582no—
158C2×C8—292no—
159C2×C8—584no—
160C2×C8C22×D2912yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—292no—
165C4⋊C4—582no—
166C4⋊C4—582no—
167C4⋊C4—582no—
168C4⋊C4—582no—
169C4⋊C4—581no—
170C4⋊C4—581no—
171C4⋊C4—581no—
172C4⋊C4C22×D2912yes—
173C42—291no—
174C42—291no—
175C42—291no—
176C42C22×D2911yescharacteristic
177C23—291no—
178Q8—24no—
179Q8—42no—
180Q8—584no—
181Q8—1164no—
182Q8—1164no—
183Q8—1162no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—291no—
187C2×C4—291no—
188C2×C4—291no—
189C2×C4—294no—
190C2×C4—294no—
191C2×C4—294no—
192C2×C4—582no—
193C2×C4—582no—
194C2×C4—1164no—
195C2×C4—1164no—
196C2×C4D4×D2911yescharacteristic
197C2×C4D4×D2911yescharacteristic
198C2×C4C23×D2911yescharacteristic
199C8—22no—
200C8—582no—
201C22—292no—
202C22—292no—
203C22—292no—
204C22C2×D4×D2911yescharacteristic
205C4—42no—
206C4—42no—
207C4—292no—
208C4—292no—
209C4—292no—
210C4—1162no—
211C4—1162no—
212C4SD16×D2912yes—
213C4Q16×D2912yes—
214C4#41×D2912yes—
215C2—294no—
216C2#124×D2911yescharacteristic
217C2C2×SD16×D2911yescharacteristic
218C2C2×Q16×D2911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#487C2
socleC22×C29C22×D4
prime radicalC22×D29C2×D4
hypercenter#487D29
hypocenterC29C2×#487
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #14271515C2semidirect
4. #14271514C2semidirect
5. #14271513C2semidirect
6. #14271512C2semidirect
9. C29×#487C2semidirect
112. #487D29direct (N × H)
118. D29#487direct (N × H)
144. C29C2×#487semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D292
#142715152
#142715142
#142715132
#142715122
#103×D292
C4×C8×D292
C29×#4872
C2×#48729