Finite Group Databasebeta

← D29⋊#352 #16835741

Subgroups — D29⋊#352 #16835741

Order 3712.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D29⋊#100C211yesmaximal, characteristic
2D29⋊#99C211yesmaximal, characteristic
3#14272066C212yesmaximal, complemented
4#14272065C212yesmaximal, complemented
5#123×D29C211yesmaximal, characteristic
6C2×D4×D29C2211yescharacteristic
7C22×C4×D29C411yescharacteristic, complemented
8C2×C22⋊#1181—21no—
9D29⋊M16—21no—
10C29×#123C411yescharacteristic, complemented
11#11745297C411yescharacteristic, complemented
12#11745291C2211yescharacteristic
13#11745256—21no—
14C4⋊C4×D29—21no—
15#11745248C2211yescharacteristic
16#11745245—21no—
17C22⋊C4×D29—21no—
18C22⋊C4×D29C411yescharacteristic, complemented
19#11745229—21no—
20#11745229C2212yes—
21#11745227C2212yes—
22#11745215—21no—
23C23×D29C2×C411yescharacteristic
24C23×D29D411yescharacteristic
25C22×#1181—41no—
26C2×D4×C29C2×C411yescharacteristic
27C22×C4×C29C2×C411yescharacteristic, complemented
28C2×C22⋊D29D411yescharacteristic
29C2×C22⋊D29C2311yescharacteristic
30C22×Dic29C2×C411yescharacteristic, complemented
31D4×D29—41no—
32D4×D29—41no—
33C2×D116D411yescharacteristic
34C2×C4×D29—21no—
35C2×C4×D29—21no—
36C2×C4×D29—21no—
37C2×C4×D29—41no—
38C2×C4×D29—41no—
39C2×C4×D29D411yescharacteristic
40C22⋊#1181—22no—
41C22⋊#1181—41no—
42#90800—22no—
43#90796—41no—
44D29⋊C8—41no—
45C4⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29C2×C411yescharacteristic, complemented
48C22⋊Dic29—21no—
49C22⋊Dic29C2×C411yescharacteristic, complemented
50#90781—21no—
51#90781—21no—
52#90781—21no—
53C4⋊Dic29—21no—
54#90779—21no—
55#90779—21no—
56C23×C29C22⋊C411yescharacteristic
57C23×C29C22×C411yescharacteristic
58C22×D29—21no—
59C22×D29—21no—
60C22×D29—21no—
61C22×D29—21no—
62C22×D29—42no—
63C22×D29—42no—
64C22×D29C22⋊C411yescharacteristic
65C22×D29C22⋊C411yescharacteristic
66C22×D29C2×D411yescharacteristic
67C2×#1181—42no—
68C2×#1181—82no—
69D4×C29—41no—
70C2×C4×C29—21no—
71C2×C4×C29—21no—
72C2×C4×C29—41no—
73C2×C4×C29C22⋊C411yescharacteristic
74C22⋊D29—41no—
75C22⋊D29—41no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—41no—
79C2×Dic29C2×D411yescharacteristic
80D116—41no—
81C4×D29—21no—
82C4×D29—21no—
83C4×D29—42no—
84C4×D29—42no—
85C4×D29—41no—
86C4×D29—41no—
87#6599—42no—
88C2×#352—291nomaximal, Sylow
89C22×C29—21no—
90C22×C29—21no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29C2×C22⋊C411yescharacteristic
94C2×D29—22no—
95C2×D29—21no—
96C2×D29—21no—
97C2×D29—42no—
98C2×D29—42no—
99C2×D29—42no—
100C2×D29—41no—
101C2×D29—41no—
102C2×D29—81no—
103C2×D29#9911yescharacteristic
104C2×D29#9911yescharacteristic
105#1181—82no—
106C4×C29—21no—
107C4×C29—41no—
108C4×C29—41no—
109Dic29—21no—
110Dic29—41no—
111Dic29—41no—
112C2×#123—291no—
113C2×#100—291no—
114C2×#99—291no—
115#352—292no—
116#352—292no—
117C2×C29—21no—
118C2×C29—41no—
119C2×C29—41no—
120C2×C29C2×#9911yescharacteristic
121D29—21no—
122D29—41no—
123D29—41no—
124D29#35212yescomplemented
125C22×D4—291no—
126C23×C4—291no—
127C2×M16—581no—
128#123—291no—
129#123—291no—
130#123—291no—
131#123—581no—
132#123—581no—
133#123#118111yescharacteristic, complemented
134C2×C4⋊C4—581no—
135C2×C22⋊C4—291no—
136C2×C22⋊C4—581no—
137C2×C22⋊C4—581no—
138#100—292no—
139#100—581no—
140#99—292no—
141#99—581no—
142C29C2×#35211yescharacteristic, complemented, Sylow
143C24—291no—
144C24—291no—
145C2×D4—291no—
146C2×D4—291no—
147C2×D4—291no—
148C2×D4—1161no—
149C2×D4—1161no—
150C2×D4C2×#118111yescharacteristic
151C22×C4—291no—
152C22×C4—291no—
153C22×C4—581no—
154C22×C4—581no—
155C22×C4—581no—
156C22×C4—1161no—
157C22×C4—1161no—
158C22×C4—1161no—
159C22×C4C2×#118111yescharacteristic, complemented
160M16—582no—
161M16—1161no—
162C2×C8—1161no—
163C4⋊C4—21no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—581no—
167C22⋊C4—21no—
168C22⋊C4—291no—
169C22⋊C4—581no—
170C22⋊C4—581no—
171C22⋊C4—581no—
172C22⋊C4—581no—
173C22⋊C4—582no—
174C22⋊C4—1161no—
175C22⋊C4C2×#118111yescharacteristic, complemented
176C23—291no—
177C23—291no—
178C23—291no—
179C23—581no—
180C23—581no—
181C23—581no—
182C23—581no—
183C23—1162no—
184C23—1162no—
185C23C22⋊#118111yescharacteristic
186C23C22×#118111yescharacteristic
187D4—41no—
188D4—1161no—
189D4—1161no—
190D4—1161no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—291no—
195C2×C4—581no—
196C2×C4—581no—
197C2×C4—581no—
198C2×C4—581no—
199C2×C4—1161no—
200C2×C4—1161no—
201C2×C4—1162no—
202C2×C4—1162no—
203C2×C4—1161no—
204C2×C4—1162no—
205C2×C4—2322no—
206C2×C4C22⋊#118111yescharacteristic
207C8—1162no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—291no—
213C22—291no—
214C22—582no—
215C22—581no—
216C22—581no—
217C22—1161no—
218C22—1161no—
219C22—1162no—
220C22—1162no—
221C22—1162no—
222C22—2321no—
223C22C2×C22⋊#118111yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—581no—
228C4—1161no—
229C4—1161no—
230C4—2322no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—292no—
235C2—581no—
236C2—1161no—
237C2—1161no—
238C2D29⋊#9911yescharacteristic
subgroupG/H
centerC2D29⋊#99
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC29×#123C4
socleC2×C29C2×#99
prime radicalC2×D4×D29C22
cosocleC2×C22⋊D29C23
hypercenter#123#1181
hypocenterC29C2×#352
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #14272066C2semidirect
4. #14272065C2semidirect
7. C22×C4×D29C4semidirect
10. C29×#123C4semidirect
11. #11745297C4semidirect
18. C22⋊C4×D29C4semidirect
27. C22×C4×C29C2×C4semidirect
30. C22×Dic29C2×C4semidirect
47. C22⋊C4×C29C2×C4semidirect
49. C22⋊Dic29C2×C4semidirect
124. D29#352semidirect
133. #123#1181semidirect
142. C29C2×#352semidirect
159. C22×C4C2×#1181semidirect
175. C22⋊C4C2×#1181semidirect

Maximal subgroups

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

subgroupindex
D29⋊#1002
D29⋊#992
#142720662
#142720652
#123×D292
C2×#35229