Finite Group Databasebeta

← C29×#12308 #20307208

Subgroups — C29×#12308 #20307208

Order 7424.

274 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 70 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×#3255C211yesmaximal, characteristic
2C29×#2239C212yesmaximal
3C29×#2102C211yesmaximal, characteristic
4C29×#1340C212yesmaximal
5C29×#1327C211yesmaximal, characteristic
6C29×#533—21no—
7C29×#475—22no—
8C29×#470—21no—
9C29×#470C2212yes—
10C29×#462—22no—
11C29×#430C2211yescharacteristic
12C29×#423C2211yescharacteristic
13C29×#365—22no—
14C29×#362—22no—
15C29×#349C2212yes—
16C29×#344—21no—
17C29×#339—21no—
18C29×H(3,ℤ/4)C2211yescharacteristic
19C2×Q16×C29—21no—
20C2×Q16×C29D412yes—
21C2×M16×C29—21no—
22C2×M16×C29D411yescharacteristic
23C2×M16×C29C2311yescharacteristic
24C29×C4⋊Q8—21no—
25C29×C4⋊Q8—21no—
26C29×#125—41no—
27C29×C22⋊Q8—22no—
28C29×C22⋊Q8—41no—
29C4×Q8×C29—22no—
30C4×Q8×C29—41no—
31C29×#117—21no—
32C29×#117—41no—
33C2×C42×C29D411yescharacteristic
34C29×M32—22no—
35C29×#108—22no—
36C29×#106—21no—
37C29×#106D412yes—
38C29×C4⋊C8—22no—
39C29×#103—22no—
40C29×#103—22no—
41C2×Q8×C29—22no—
42C2×Q8×C29—41no—
43C22×C4×C29—21no—
44C22×C4×C29C2×D411yescharacteristic
45Q16×C29—42no—
46Q16×C29—81no—
47M16×C29—41no—
48M16×C29—41no—
49M16×C29—41no—
50M16×C29—41no—
51C2×C8×C29—21no—
52C2×C8×C29—41no—
53C2×C8×C29C2×D412yes—
54C4⋊C4×C29—22no—
55C4⋊C4×C29—41no—
56C4⋊C4×C29—41no—
57C4⋊C4×C29—42no—
58C4⋊C4×C29—41no—
59C4⋊C4×C29—41no—
60C4⋊C4×C29—42no—
61C22⋊C4×C29—42no—
62C22⋊C4×C29—41no—
63C42×C29—21no—
64C42×C29—42no—
65C42×C29—41no—
66C42×C29SD1611yescharacteristic
67C42×C29SD1611yescharacteristic
68C16×C29—42no—
69#12308C2911yesmaximal, characteristic, direct product factor, Sylow
70C23×C29AGL(1,ℤ/8)11yescharacteristic
71Q8×C29—42no—
72Q8×C29—42no—
73Q8×C29—82no—
74C2×C4×C29—21no—
75C2×C4×C29—21no—
76C2×C4×C29—21no—
77C2×C4×C29—21no—
78C2×C4×C29—42no—
79C2×C4×C29—42no—
80C2×C4×C29—42no—
81C2×C4×C29—81no—
82C2×C4×C29#12011yescharacteristic
83C2×C4×C29C2×SD1611yescharacteristic
84C8×C29—22no—
85C8×C29—41no—
86C8×C29—81no—
87#3255C2×C2911yescharacteristic
88#2239C2×C2912yes—
89#2102C2×C2911yescharacteristic
90#1340C2×C2912yes—
91#1327C2×C2911yescharacteristic
92C22×C29—21no—
93C22×C29—41no—
94C22×C29#45011yescharacteristic
95C4×C29—22no—
96C4×C29—21no—
97C4×C29—41no—
98C4×C29—82no—
99C4×C29—82no—
100C4×C29—161no—
101C4×C29#45411yescharacteristic
102C4×C29#45811yescharacteristic
103#533—21no—
104#475—22no—
105#470—21no—
106#470C22×C2912yes—
107#462—22no—
108#430C22×C2911yescharacteristic
109#423C22×C2911yescharacteristic
110#365—22no—
111#362—22no—
112#349C22×C2912yes—
113#344—21no—
114#339—21no—
115H(3,ℤ/4)C22×C2911yescharacteristic
116C2×C29—21no—
117C2×C29—41no—
118C2×C29#161611yescharacteristic
119C2×Q16—21no—
120C2×Q16D4×C2912yes—
121C2×M16—21no—
122C2×M16D4×C2911yescharacteristic
123C2×M16C23×C2911yescharacteristic
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126#125—41no—
127C22⋊Q8—22no—
128C22⋊Q8—41no—
129C4×Q8—22no—
130C4×Q8—41no—
131#117—21no—
132#117—41no—
133C2×C42D4×C2911yescharacteristic
134M32—22no—
135#108—22no—
136#106—21no—
137#106D4×C2912yes—
138C4⋊C8—22no—
139#103—22no—
140#103—22no—
141C29#1230811yescharacteristic, direct product factor, Sylow
142C2×Q8—22no—
143C2×Q8—41no—
144C22×C4—21no—
145C22×C4C2×D4×C2911yescharacteristic
146Q16—42no—
147Q16—81no—
148M16—41no—
149M16—41no—
150M16—41no—
151M16—41no—
152C2×C8—21no—
153C2×C8—41no—
154C2×C8C2×D4×C2912yes—
155C4⋊C4—22no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—42no—
162C22⋊C4—42no—
163C22⋊C4—41no—
164C42—21no—
165C42—42no—
166C42—41no—
167C42SD16×C2911yescharacteristic
168C42SD16×C2911yescharacteristic
169C16—42no—
170C23C29×AGL(1,ℤ/8)11yescharacteristic
171Q8—42no—
172Q8—42no—
173Q8—82no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—81no—
182C2×C4C29×#12011yescharacteristic
183C2×C4C2×SD16×C2911yescharacteristic
184C8—22no—
185C8—41no—
186C8—81no—
187C22—21no—
188C22—41no—
189C22C29×#45011yescharacteristic
190C4—22no—
191C4—21no—
192C4—41no—
193C4—82no—
194C4—82no—
195C4—161no—
196C4C29×#45411yescharacteristic
197C4C29×#45811yescharacteristic
198C2—21no—
199C2—41no—
200C2C29×#161611yescharacteristic
subgroupG/H
center, socleC2×C29#1616
commutator, Frattini, cosocleC2×M16C23×C29
prime radicalC23×C29AGL(1,ℤ/8)
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×M16×C29 ◁ G

Complements

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

NH ≅ G/Ntype
69. #12308C29direct (N × H)
141. C29#12308direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32552
C29×#22392
C29×#21022
C29×#13402
C29×#13272
#1230829