Finite Group Databasebeta

← D29×#328 #16817971

Subgroups — D29×#328 #16817971

Order 3712.

336 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C22⋊Q8×D29C211yesmaximal, characteristic
2C22⋊C8×D29C211yesmaximal, characteristic
3#95×D29C211yesmaximal, characteristic
4#14270901C211yesmaximal, characteristic, complemented
5#14270900C211yesmaximal, characteristic, complemented
6#14270899C211yesmaximal, characteristic, complemented
7C29×#328C211yesmaximal, characteristic, complemented
8C2×Q8×D29C411yescharacteristic, complemented
9C22×C4×D29—21no—
10C22×C4×D29C2211yescharacteristic
11C29×C22⋊Q8C2211yescharacteristic
12#11745308C411yescharacteristic, complemented
13#11745286C2211yescharacteristic
14C2×C8×D29—21no—
15#11745259C411yescharacteristic, complemented
16#11745258—21no—
17C4⋊C4×D29—21no—
18C4⋊C4×D29C411yescharacteristic, complemented
19C22⋊C4×D29—21no—
20#11745240—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179—21no—
24#11745179C2211yescharacteristic
25C22⋊#6597C2211yescharacteristic
26#11745168—21no—
27C23×D29D411yescharacteristic
28C2×Q8×C29C2×C411yescharacteristic, complemented
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C22×Dic29—21no—
32C22×Dic29D411yescharacteristic
33Q8×D29—42no—
34C2×C4×D29—24no—
35C2×C4×D29—21no—
36C2×C4×D29—21no—
37C2×C4×D29—42no—
38C2×C4×D29—42no—
39C2×C4×D29—42no—
40C2×C4×D29C2×C411yescharacteristic
41C2×C4×D29C2×C411yescharacteristic
42C2×C4×D29D411yescharacteristic
43C2×C4×D29D411yescharacteristic
44C2×Dic58—21no—
45C2×Dic58C2×C411yescharacteristic, complemented
46C2×C8×C29—21no—
47C4⋊C4×C29—21no—
48C4⋊C4×C29C2×C411yescharacteristic, complemented
49C22⋊C4×C29—21no—
50C22⋊Dic29—21no—
51#90781—21no—
52#90781—21no—
53C4⋊Dic29—21no—
54C4⋊Dic29C2×C411yescharacteristic, complemented
55#90779—21no—
56#90779—21no—
57#90779—21no—
58C2×#6597—21no—
59C8×D29—42no—
60C23×C29C2×D411yescharacteristic
61C22×D29—22no—
62C22×D29—22no—
63C22×D29C22⋊C411yescharacteristic
64C22×D29C22⋊C411yescharacteristic
65C22×D29SD1612yes—
66C22×D29Q1612yes—
67Q8×C29—41no—
68C2×C4×C29—22no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—41no—
72C2×C4×C29—41no—
73C2×C4×C29—41no—
74C2×C4×C29C22×C411yescharacteristic
75C2×C4×C29C2×D411yescharacteristic
76C2×Dic29—22no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29—41no—
82C2×Dic29C22⋊C411yescharacteristic
83C2×Dic29C22⋊C411yescharacteristic
84C4×D29—22no—
85C4×D29—22no—
86C4×D29—41no—
87C4×D29—41no—
88C4×D29—48no—
89C4×D29—42no—
90C4×D29—42no—
91Dic58—42no—
92Dic58—41no—
93C8×C29—41no—
94#6597—41no—
95C2×#328—291nomaximal, Sylow
96C22×C29—21no—
97C22×C29—21no—
98C22×C29C2×C22⋊C411yescharacteristic
99C22×C29C2×SD1611yescharacteristic
100C22×C29C2×Q1611yescharacteristic
101C2×D29—21no—
102C2×D29—21no—
103C2×D29—24no—
104C2×D29—24no—
105C2×D29#9912yes—
106C2×D29#10312yes—
107C2×D29#10312yes—
108C2×D29#10412yes—
109C4×C29—21no—
110C4×C29—21no—
111C4×C29—42no—
112C4×C29—41no—
113C4×C29—41no—
114Dic29—21no—
115Dic29—21no—
116Dic29—42no—
117Dic29—41no—
118Dic29—41no—
119C2×C22⋊Q8—291no—
120C2×C22⋊C8—291no—
121C2×#95—291no—
122#328—291no—
123#328—291no—
124#328—291no—
125#328D2911yescharacteristic, direct product factor
126C2×C29—21no—
127C2×C29—21no—
128C2×C29C2×#9911yescharacteristic
129C2×C29C2×#10311yescharacteristic
130C2×C29C2×#10411yescharacteristic
131D29—22no—
132D29#32814yesdirect product factor
133C22×Q8—291no—
134C23×C4—291no—
135C23×C4—581no—
136C22×C8—581no—
137C22⋊Q8—291no—
138C22⋊Q8—291no—
139C22⋊Q8—291no—
140C22⋊Q8—581no—
141C22⋊Q8—581no—
142C22⋊Q8C2×D2911yescharacteristic
143C2×C4⋊C4—291no—
144C2×C4⋊C4—581no—
145C2×C22⋊C4—581no—
146C22⋊C8—291no—
147C22⋊C8—581no—
148C22⋊C8C2×D2911yescharacteristic
149#95—291no—
150#95—581no—
151#95C2×D2911yescharacteristic
152C29C2×#32811yescharacteristic, complemented, Sylow
153C24—291no—
154C2×Q8—291no—
155C2×Q8—581no—
156C2×Q8—1162no—
157C2×Q8C4×D2911yescharacteristic, complemented
158C22×C4—21no—
159C22×C4—291no—
160C22×C4—291no—
161C22×C4—291no—
162C22×C4—291no—
163C22×C4—291no—
164C22×C4—581no—
165C22×C4—581no—
166C22×C4—584no—
167C22×C4—581no—
168C22×C4—1162no—
169C22×C4—1162no—
170C22×C4—1162no—
171C22×C4C22×D2911yescharacteristic
172C2×C8—21no—
173C2×C8—581no—
174C2×C8—1162no—
175C4⋊C4—21no—
176C4⋊C4—291no—
177C4⋊C4—581no—
178C4⋊C4—581no—
179C4⋊C4—581no—
180C4⋊C4—581no—
181C4⋊C4C4×D2911yescharacteristic, complemented
182C22⋊C4—21no—
183C22⋊C4—581no—
184C22⋊C4—581no—
185C22⋊C4—581no—
186C23—291no—
187C23—291no—
188C23—292no—
189C23—292no—
190C23—582no—
191C23—582no—
192C23D4×D2911yescharacteristic
193Q8—41no—
194Q8—1161no—
195Q8—1162no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—291no—
203C2×C4—291no—
204C2×C4—582no—
205C2×C4—582no—
206C2×C4—582no—
207C2×C4—581no—
208C2×C4—581no—
209C2×C4—1161no—
210C2×C4—1161no—
211C2×C4—1162no—
212C2×C4—1162no—
213C2×C4—1168no—
214C2×C4—1161no—
215C2×C4—1161no—
216C2×C4—1161no—
217C2×C4C2×C4×D2911yescharacteristic
218C2×C4D4×D2911yescharacteristic
219C8—41no—
220C8—1161no—
221C22—21no—
222C22—21no—
223C22—292no—
224C22—292no—
225C22—292no—
226C22—292no—
227C22—584no—
228C22—584no—
229C22—581no—
230C22—581no—
231C22C22⋊C4×D2911yescharacteristic
232C22SD16×D2911yescharacteristic
233C22Q16×D2911yescharacteristic
234C4—21no—
235C4—21no—
236C4—42no—
237C4—41no—
238C4—41no—
239C4—581no—
240C4—581no—
241C4—1162no—
242C4—1161no—
243C4—1161no—
244C2—21no—
245C2—21no—
246C2—294no—
247C2—582no—
248C2#99×D2911yescharacteristic
249C2#103×D2911yescharacteristic
250C2#104×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29C2×C22⋊C4
prime radicalC23×D29D4
cosocleC22×C4×C29C23
hypercenter#328D29
hypocenterC29C2×#328
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. #14270901C2semidirect
5. #14270900C2semidirect
6. #14270899C2semidirect
7. C29×#328C2semidirect
8. C2×Q8×D29C4semidirect
12. #11745308C4semidirect
15. #11745259C4semidirect
18. C4⋊C4×D29C4semidirect
28. C2×Q8×C29C2×C4semidirect
45. C2×Dic58C2×C4semidirect
48. C4⋊C4×C29C2×C4semidirect
54. C4⋊Dic29C2×C4semidirect
125. #328D29direct (N × H)
132. D29#328direct (N × H)
152. C29C2×#328semidirect
157. C2×Q8C4×D29semidirect
181. C4⋊C4C4×D29semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D292
C22⋊C8×D292
#95×D292
#142709012
#142709002
#142708992
C29×#3282
C2×#32829