Finite Group Databasebeta

← C29×#2027 #16815741

Subgroups — C29×#2027 #16815741

Order 3712.

282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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×#544C211yesmaximal, characteristic, complemented
2C29×#418C212yesmaximal
3C29×#390C211yesmaximal, characteristic
4C29×#343C211yesmaximal, characteristic, complemented
5C29×#339C212yesmaximal, complemented
6C22×D4×C29C2211yescharacteristic
7C2×M16×C29C2212yes—
8C29×C4⋊Q8—22no—
9C29×#125—22no—
10C29×C22⋊Q8—22no—
11C29×#117C2212yes—
12C2×C4⋊C4×C29C2211yescharacteristic
13C2×C22⋊C4×C29—22no—
14C2×C42×C29C2211yescharacteristic
15C29×#102—22no—
16C29×#102—22no—
17C24×C29—21no—
18C2×Q8×C29—22no—
19C2×D4×C29—22no—
20C2×D4×C29—22no—
21C2×D4×C29—21no—
22C2×D4×C29Q812yescomplemented
23C22×C4×C29—21no—
24C22×C4×C29D412yes—
25C22×C4×C29C2311yescharacteristic
26M16×C29—22no—
27M16×C29—22no—
28C2×C8×C29—22no—
29C4⋊C4×C29—22no—
30C4⋊C4×C29—24no—
31C4⋊C4×C29—22no—
32C4⋊C4×C29D412yes—
33C4⋊C4×C29D412yes—
34C22⋊C4×C29—22no—
35C22⋊C4×C29—44no—
36C42×C29—22no—
37C42×C29—22no—
38C23×C29—22no—
39C23×C29—42no—
40C23×C29—42no—
41C23×C29—41no—
42C23×C29—41no—
43C23×C29C2×D411yescharacteristic
44Q8×C29—82no—
45D4×C29—24no—
46D4×C29—42no—
47C2×C4×C29—22no—
48C2×C4×C29—22no—
49C2×C4×C29—22no—
50C2×C4×C29—22no—
51C2×C4×C29—41no—
52C2×C4×C29—41no—
53C2×C4×C29—42no—
54C2×C4×C29C2×D412yes—
55C2×C4×C29C2×Q811yescharacteristic
56C2×C4×C29#4112yes—
57C2×C4×C29#4111yescharacteristic
58C8×C29—42no—
59#2027C2911yesmaximal, characteristic, direct product factor, Sylow
60C22×C29—21no—
61C22×C29—21no—
62C22×C29—44no—
63C22×C29—42no—
64C22×C29—82no—
65C22×C29—81no—
66C22×C29—81no—
67C22×C29#12011yescharacteristic
68C22×C29C22⋊Q811yescharacteristic
69C22×C29#12411yescharacteristic
70C4×C29—42no—
71C4×C29—42no—
72C4×C29—42no—
73C4×C29—42no—
74C4×C29C22⋊Q812yes—
75C4×C29#12412yes—
76#544C2×C2911yescharacteristic, complemented
77#418C2×C2912yes—
78#390C2×C2911yescharacteristic
79#343C2×C2911yescharacteristic, complemented
80#339C2×C2912yescomplemented
81C2×C29—21no—
82C2×C29—21no—
83C2×C29—82no—
84C2×C29#39311yescharacteristic
85C2×C29#45311yescharacteristic
86C2×C29#45411yescharacteristic
87C22×D4C22×C2911yescharacteristic
88C2×M16C22×C2912yes—
89C4⋊Q8—22no—
90#125—22no—
91C22⋊Q8—22no—
92#117C22×C2912yes—
93C2×C4⋊C4C22×C2911yescharacteristic
94C2×C22⋊C4—22no—
95C2×C42C22×C2911yescharacteristic
96#102—22no—
97#102—22no—
98C29#202711yescharacteristic, direct product factor, Sylow
99C24—21no—
100C2×Q8—22no—
101C2×D4—22no—
102C2×D4—22no—
103C2×D4—21no—
104C2×D4Q8×C2912yescomplemented
105C22×C4—21no—
106C22×C4D4×C2912yes—
107C22×C4C23×C2911yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—22no—
112C4⋊C4—24no—
113C4⋊C4—22no—
114C4⋊C4D4×C2912yes—
115C4⋊C4D4×C2912yes—
116C22⋊C4—22no—
117C22⋊C4—44no—
118C42—22no—
119C42—22no—
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×D4×C2911yescharacteristic
126Q8—82no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—42no—
136C2×C4C2×D4×C2912yes—
137C2×C4C2×Q8×C2911yescharacteristic
138C2×C4#41×C2912yes—
139C2×C4#41×C2911yescharacteristic
140C8—42no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22C29×#12011yescharacteristic
149C22C29×C22⋊Q811yescharacteristic
150C22C29×#12411yescharacteristic
151C4—42no—
152C4—42no—
153C4—42no—
154C4—42no—
155C4C29×C22⋊Q812yes—
156C4C29×#12412yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2C29×#39311yescharacteristic
161C2C29×#45311yescharacteristic
162C2C29×#45411yescharacteristic
subgroupG/H
center, socleC22×C29#120
commutator, Frattini, cosocleC22×C4C23×C29
prime radicalC22×D4×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#544C2semidirect
4. C29×#343C2semidirect
5. C29×#339C2semidirect
22. C2×D4×C29Q8semidirect
59. #2027C29direct (N × H)
76. #544C2×C29semidirect
79. #343C2×C29semidirect
80. #339C2×C29semidirect
98. C29#2027direct (N × H)
104. C2×D4Q8×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#5442
C29×#4182
C29×#3902
C29×#3432
C29×#3392
#202729