Finite Group Databasebeta

← D29×#355 #16821168

Subgroups — D29×#355 #16821168

Order 3712.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D29C211yesmaximal, characteristic
2#101×D29C212yesmaximal, complemented
3#14270960C211yesmaximal, characteristic, complemented
4#14270959C212yesmaximal, complemented
5C29×#355C211yesmaximal, characteristic, complemented
6C2×Q8×D29C2211yescharacteristic
7C2×D4×D29C411yescharacteristic
8C29×#124C2211yescharacteristic
9#11745309C2211yescharacteristic
10#11745298C411yescharacteristic
11M16×D29—22no—
12#11745247—22no—
13C22⋊C4×D29—22no—
14#11745237C411yescharacteristic
15C42×D29C411yescharacteristic
16C29×#101C2212yescomplemented
17#11745184C2212yescomplemented
18#11745172—22no—
19C23×D29—21no—
20C2×Q8×C29C2311yescharacteristic
21C2×D4×C29C2×C411yescharacteristic
22C2×C22⋊D29—21no—
23Q8×D29—41no—
24Q8×D29—41no—
25D4×D29—41no—
26D4×D29—41no—
27C2×D116C2×C411yescharacteristic
28C2×C4×D29—21no—
29C2×C4×D29C2×C411yescharacteristic
30C2×C4×D29D412yes—
31C2×Dic58C2×C411yescharacteristic
32C2×Dic58D412yes—
33M16×C29—22no—
34C22⋊C4×C29—22no—
35C42×C29C2×C411yescharacteristic
36C22⋊Dic29—22no—
37#90781—22no—
38#90781—22no—
39C4×Dic29—21no—
40C4×Dic29C2×C411yescharacteristic
41#90777—22no—
42#90772—42no—
43C8×D29—42no—
44C23×C29—21no—
45C22×D29—21no—
46C22×D29—44no—
47C22×D29—41no—
48C22×D29—41no—
49C22×D29C22⋊C411yescharacteristic
50Q8×C29—41no—
51D4×C29—41no—
52C2×C4×C29—21no—
53C2×C4×C29C22×C411yescharacteristic
54C2×C4×C29C2×D412yes—
55C22⋊D29—42no—
56C2×Dic29—21no—
57C2×Dic29C22⋊C411yescharacteristic
58C2×Dic29C22⋊C412yes—
59D116—41no—
60C4×D29—22no—
61C4×D29—22no—
62C4×D29—21no—
63C4×D29—21no—
64C4×D29—42no—
65Dic58—41no—
66Dic58—42no—
67C8×C29—42no—
68#6597—42no—
69C2×#355—291nomaximal, Sylow
70C22×C29—42no—
71C22×C29—41no—
72C22×C29C2×C22⋊C411yescharacteristic
73C2×D29—22no—
74C2×D29—42no—
75C2×D29—41no—
76C2×D29—82no—
77C2×D29—82no—
78C2×D29#9911yescharacteristic
79C2×D29#9911yescharacteristic
80C4×C29—22no—
81C4×C29—21no—
82C4×C29—41no—
83Dic29—22no—
84Dic29—21no—
85Dic29—41no—
86C2×#124—291no—
87C2×#101—292no—
88#355—291no—
89#355—292no—
90#355D2911yescharacteristic, direct product factor
91C2×C29—21no—
92C2×C29—81no—
93C2×C29C2×#9911yescharacteristic
94D29—21no—
95D29—81no—
96D29#35512yesdirect product factor
97C22×Q8—291no—
98C22×D4—291no—
99C2×M16—582no—
100#124—291no—
101#124—291no—
102#124—291no—
103#124—582no—
104#124C2×D2911yescharacteristic
105C2×C22⋊C4—582no—
106C2×C42—291no—
107#101—292no—
108#101—582no—
109#101C2×D2912yescomplemented
110C29C2×#35511yescharacteristic, complemented, Sylow
111C24—581no—
112C2×Q8—291no—
113C2×Q8—292no—
114C2×Q8—1161no—
115C2×Q8—1161no—
116C2×Q8C22×D2911yescharacteristic
117C2×D4—291no—
118C2×D4—581no—
119C2×D4—1161no—
120C2×D4—1161no—
121C2×D4C4×D2911yescharacteristic
122C22×C4—291no—
123C22×C4—292no—
124C22×C4—581no—
125M16—22no—
126M16—582no—
127M16—1162no—
128C2×C8—1162no—
129C22⋊C4—22no—
130C22⋊C4—582no—
131C22⋊C4—582no—
132C22⋊C4—582no—
133C42—291no—
134C42—581no—
135C42C4×D2911yescharacteristic
136C23—21no—
137C23—291no—
138C23—581no—
139C23—1161no—
140C23—1161no—
141C23—1164no—
142Q8—41no—
143Q8—1162no—
144Q8—1161no—
145D4—41no—
146D4—1161no—
147D4—1162no—
148C2×C4—21no—
149C2×C4—291no—
150C2×C4—292no—
151C2×C4—582no—
152C2×C4—582no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—581no—
156C2×C4—1162no—
157C2×C4C2×C4×D2911yescharacteristic
158C2×C4D4×D2912yes—
159C8—42no—
160C8—1162no—
161C22—42no—
162C22—41no—
163C22—291no—
164C22—291no—
165C22—582no—
166C22—1162no—
167C22—1161no—
168C22—2322no—
169C22—2322no—
170C22C22⋊C4×D2911yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—581no—
175C4—582no—
176C4—1161no—
177C2—21no—
178C2—81no—
179C2—292no—
180C2—581no—
181C2—2321no—
182C2#99×D2911yescharacteristic
subgroupG/H
centerC2#99×D29
commutatorC2×C4×C29C22×C4
FrattiniC2×Q8C22×D29
FittingC29×#355C2
socleC2×C29C2×#99
prime radicalC2×D4×D29C4
cosocleC2×Q8×C29C23
hypercenter#355D29
hypocenterC29C2×#355
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D29C2semidirect
3. #14270960C2semidirect
4. #14270959C2semidirect
5. C29×#355C2semidirect
16. C29×#101C22semidirect
17. #11745184C22semidirect
90. #355D29direct (N × H)
96. D29#355direct (N × H)
109. #101C2×D29semidirect
110. C29C2×#355semidirect

Maximal subgroups

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

subgroupindex
#124×D292
#101×D292
#142709602
#142709592
C29×#3552
C2×#35529