Finite Group Databasebeta

← C29×#1613 #16815327

Subgroups — C29×#1613 #16815327

Order 3712.

288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C29×#534C211yesmaximal, characteristic
2C29×#481C212yesmaximal, complemented
3C29×#399C211yesmaximal, characteristic, complemented
4C29×#327C212yesmaximal, complemented
5C29×#323C211yesmaximal, characteristic, complemented
6C22×D4×C29—21no—
7C29×#123—22no—
8C29×#121—21no—
9C29×#121C2212yes—
10C29×#120—22no—
11C2×C4⋊C4×C29—21no—
12C2×C4⋊C4×C29C2211yescharacteristic, complemented
13C2×C22⋊C4×C29—21no—
14C2×C22⋊C4×C29C2211yescharacteristic
15C29×#106—22no—
16C29×#102—22no—
17C29×C22⋊C8C2212yescomplemented
18C29×#95C2211yescharacteristic, complemented
19C24×C29—21no—
20C24×C29D411yescharacteristic
21C2×D4×C29—22no—
22C2×D4×C29—22no—
23C2×D4×C29—21no—
24C2×D4×C29—42no—
25C2×D4×C29—42no—
26C2×D4×C29D412yes—
27C22×C4×C29—21no—
28C22×C4×C29—21no—
29C22×C4×C29—21no—
30C22×C4×C29D411yescharacteristic
31C22×C4×C29C2311yescharacteristic
32C2×C8×C29—22no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—22no—
35C4⋊C4×C29—42no—
36C4⋊C4×C29D412yes—
37C22⋊C4×C29—22no—
38C22⋊C4×C29—22no—
39C22⋊C4×C29—22no—
40C22⋊C4×C29—42no—
41C23×C29—21no—
42C23×C29—21no—
43C23×C29—22no—
44C23×C29—41no—
45C23×C29—41no—
46C23×C29—42no—
47C23×C29—81no—
48C23×C29—81no—
49C23×C29SD1612yes—
50C23×C29C2×D411yescharacteristic
51D4×C29—42no—
52D4×C29—44no—
53D4×C29—42no—
54D4×C29—42no—
55D4×C29—81no—
56C2×C4×C29—22no—
57C2×C4×C29—21no—
58C2×C4×C29—22no—
59C2×C4×C29—41no—
60C2×C4×C29—41no—
61C2×C4×C29—42no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29C2×D412yes—
68C8×C29—42no—
69#1613C2911yesmaximal, characteristic, direct product factor, Sylow
70C22×C29—21no—
71C22×C29—21no—
72C22×C29—22no—
73C22×C29—42no—
74C22×C29—41no—
75C22×C29—41no—
76C22×C29—42no—
77C22×C29—42no—
78C22×C29—42no—
79C22×C29—81no—
80C22×C29—84no—
81C22×C29#12011yescharacteristic
82C22×C29C2×SD1611yescharacteristic
83C22×C29AGL(1,ℤ/8)11yescharacteristic
84C4×C29—22no—
85C4×C29—42no—
86C4×C29—42no—
87C4×C29—41no—
88C4×C29—81no—
89#534C2×C2911yescharacteristic
90#481C2×C2912yescomplemented
91#399C2×C2911yescharacteristic, complemented
92#327C2×C2912yescomplemented
93#323C2×C2911yescharacteristic, complemented
94C2×C29—21no—
95C2×C29—21no—
96C2×C29—42no—
97C2×C29—82no—
98C2×C29#45011yescharacteristic
99C2×C29#45311yescharacteristic
100C2×C29#45811yescharacteristic
101C22×D4—21no—
102#123—22no—
103#121—21no—
104#121C22×C2912yes—
105#120—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4C22×C2911yescharacteristic, complemented
108C2×C22⋊C4—21no—
109C2×C22⋊C4C22×C2911yescharacteristic
110#106—22no—
111#102—22no—
112C22⋊C8C22×C2912yescomplemented
113#95C22×C2911yescharacteristic, complemented
114C29#161311yescharacteristic, direct product factor, Sylow
115C24—21no—
116C24D4×C2911yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4—21no—
120C2×D4—42no—
121C2×D4—42no—
122C2×D4D4×C2912yes—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4D4×C2911yescharacteristic
127C22×C4C23×C2911yescharacteristic
128C2×C8—22no—
129C4⋊C4—21no—
130C4⋊C4—22no—
131C4⋊C4—42no—
132C4⋊C4D4×C2912yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—42no—
137C23—21no—
138C23—21no—
139C23—22no—
140C23—41no—
141C23—41no—
142C23—42no—
143C23—81no—
144C23—81no—
145C23SD16×C2912yes—
146C23C2×D4×C2911yescharacteristic
147D4—42no—
148D4—44no—
149D4—42no—
150D4—42no—
151D4—81no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4C2×D4×C2912yes—
164C8—42no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—81no—
175C22—84no—
176C22C29×#12011yescharacteristic
177C22C2×SD16×C2911yescharacteristic
178C22C29×AGL(1,ℤ/8)11yescharacteristic
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—81no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—82no—
188C2C29×#45011yescharacteristic
189C2C29×#45311yescharacteristic
190C2C29×#45811yescharacteristic
subgroupG/H
center, socleC22×C29#120
commutator, Frattini, cosocleC22×C4C23×C29
prime radicalC29×#534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#481C2semidirect
3. C29×#399C2semidirect
4. C29×#327C2semidirect
5. C29×#323C2semidirect
12. C2×C4⋊C4×C29C22semidirect
17. C29×C22⋊C8C22semidirect
18. C29×#95C22semidirect
69. #1613C29direct (N × H)
90. #481C2×C29semidirect
91. #399C2×C29semidirect
92. #327C2×C29semidirect
93. #323C2×C29semidirect
107. C2×C4⋊C4C22×C29semidirect
112. C22⋊C8C22×C29semidirect
113. #95C22×C29semidirect
114. C29#1613direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5342
C29×#4812
C29×#3992
C29×#3272
C29×#3232
#161329