Finite Group Databasebeta

← C29×#36640 #20331540

Subgroups — C29×#36640 #20331540

Order 7424.

1990 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2864C214yesmaximal, complemented
2C29×#2859C214yesmaximal, complemented
3C29×#2851C218yesmaximal
4C4×C29×#125C218yesmaximal, complemented
5C29×#2296C214yesmaximal
6C29×#2285C212yesmaximal
7C2×C43×C29C211yesmaximal, characteristic
8C2×C29×#125C2218yes—
9C2×C29×#117C2214yes—
10C22×C42×C29C2212yes—
11C22×C42×C29C2214yes—
12C22×C42×C29C2211yescharacteristic
13C29×#389C22116yes—
14C29×#389C22116yes—
15C29×#387C22132yes—
16C29×#385C22116yes—
17C29×#384C2214yes—
18C29×#382C2214yes—
19C29×#382C2218yes—
20C29×#380C2218yes—
21C4×C4⋊C4×C29C2218yes—
22C4×C4⋊C4×C29C22116yes—
23C43×C29C2214yes—
24C43×C29C2212yes—
25C43×C29C2212yes—
26C23×C4×C29C2314yes—
27C23×C4×C29C2312yes—
28C23×C4×C29C2311yescharacteristic
29C29×#125—232no—
30C29×#117—216no—
31C2×C4⋊C4×C29C2318yes—
32C2×C4⋊C4×C29C23116yes—
33C2×C4⋊C4×C29C23132yes—
34C2×C22⋊C4×C29C2318yes—
35C2×C42×C29—28no—
36C2×C42×C29—216no—
37C2×C42×C29Q818yes—
38C2×C42×C29C2318yes—
39C2×C42×C29C2314yes—
40C2×C42×C29C2314yes—
41C2×C42×C29C2314yes—
42C2×C42×C29C2318yes—
43C2×C42×C29C2311yescharacteristic
44C2×C42×C29C2311yescharacteristic
45C2×C42×C29C2312yes—
46C2×C42×C29C2314yes—
47C29×#95C23116yes—
48C29×#95C23132yes—
49C24×C29C2411yescharacteristic
50C22×C4×C29—28no—
51C22×C4×C29—216no—
52C22×C4×C29—28no—
53C22×C4×C29C2×Q818yes—
54C22×C4×C29C2×Q814yes—
55C22×C4×C29#4118yes—
56C22×C4×C29C24116yes—
57C22×C4×C29C2412yes—
58C22×C4×C29C2418yes—
59C22×C4×C29C2411yescharacteristic
60C22×C4×C29C2412yes—
61C22×C4×C29C2411yescharacteristic
62C4⋊C4×C29—216no—
63C4⋊C4×C29—264no—
64C4⋊C4×C29—232no—
65C22⋊C4×C29—216no—
66C42×C29—216no—
67C42×C29—28no—
68C42×C29—28no—
69C42×C29—28no—
70C42×C29—216no—
71C42×C29C2×Q814yes—
72C42×C29C2×Q818yes—
73C42×C29C2×Q814yes—
74C42×C29#41116yes—
75#36640C2911yesmaximal, characteristic, direct product factor, Sylow
76C23×C29—24no—
77C23×C29C22×Q812yes—
78C23×C29C2×#4114yes—
79C23×C29C2511yescharacteristic
80C2×C4×C29—232no—
81C2×C4×C29—24no—
82C2×C4×C29—28no—
83C2×C4×C29—28no—
84C2×C4×C29—216no—
85C2×C4×C29—216no—
86C2×C4×C29—232no—
87C2×C4×C29#125116yescomplemented
88C2×C4×C29C22×Q814yes—
89C2×C4×C29C22×Q812yes—
90C2×C4×C29C22×Q812yes—
91C2×C4×C29C22×Q814yes—
92C2×C4×C29C2×#41116yes—
93C2×C4×C29C2×#4114yes—
94C2×C4×C29C2×#4114yes—
95C2×C4×C29C2×#4118yes—
96#2864C2×C2914yescomplemented
97#2859C2×C2914yescomplemented
98#2851C2×C2918yes—
99C4×#125C2×C2918yescomplemented
100#2296C2×C2914yes—
101#2285C2×C2912yes—
102C2×C43C2×C2911yescharacteristic
103C22×C29—24no—
104C22×C29—28no—
105C22×C29C2×#12514yes—
106C22×C29C23×Q811yescharacteristic
107C22×C29C22×#4112yes—
108C22×C29C22×#4114yes—
109C4×C29—24no—
110C4×C29—216no—
111C4×C29—416no—
112C4×C29C2×#12514yes—
113C4×C29C2×#12514yes—
114C4×C29#53318yes—
115C2×#125C22×C2918yes—
116C2×#117C22×C2914yes—
117C22×C42C22×C2914yes—
118C22×C42C22×C2912yes—
119C22×C42C22×C2911yescharacteristic
120#389C22×C29116yes—
121#389C22×C29116yes—
122#387C22×C29132yes—
123#385C22×C29116yes—
124#384C22×C2914yes—
125#382C22×C2918yes—
126#382C22×C2914yes—
127#380C22×C2918yes—
128C4×C4⋊C4C22×C2918yes—
129C4×C4⋊C4C22×C29116yes—
130C43C22×C2914yes—
131C43C22×C2912yes—
132C43C22×C2912yes—
133C2×C29—24no—
134C2×C29C22×#12511yescharacteristic
135C2×C29C2×#53312yes—
136C2×C29#344414yes—
137C23×C4C23×C2914yes—
138C23×C4C23×C2912yes—
139C23×C4C23×C2911yescharacteristic
140#125—232no—
141#117—216no—
142C2×C4⋊C4C23×C2918yes—
143C2×C4⋊C4C23×C29116yes—
144C2×C4⋊C4C23×C29132yes—
145C2×C22⋊C4C23×C2918yes—
146C2×C42—28no—
147C2×C42—216no—
148C2×C42Q8×C2918yes—
149C2×C42C23×C2918yes—
150C2×C42C23×C2914yes—
151C2×C42C23×C2918yes—
152C2×C42C23×C2914yes—
153C2×C42C23×C2914yes—
154C2×C42C23×C2912yes—
155C2×C42C23×C2911yescharacteristic
156C2×C42C23×C2911yescharacteristic
157C2×C42C23×C2914yes—
158#95C23×C29116yes—
159#95C23×C29132yes—
160C29#3664011yescharacteristic, direct product factor, Sylow
161C24C24×C2911yescharacteristic
162C22×C4—28no—
163C22×C4—216no—
164C22×C4—28no—
165C22×C4C2×Q8×C2918yes—
166C22×C4C2×Q8×C2914yes—
167C22×C4#41×C2918yes—
168C22×C4C24×C29116yes—
169C22×C4C24×C2912yes—
170C22×C4C24×C2918yes—
171C22×C4C24×C2911yescharacteristic
172C22×C4C24×C2911yescharacteristic
173C22×C4C24×C2912yes—
174C4⋊C4—216no—
175C4⋊C4—264no—
176C4⋊C4—232no—
177C22⋊C4—216no—
178C42—216no—
179C42—28no—
180C42—28no—
181C42—28no—
182C42—216no—
183C42C2×Q8×C2914yes—
184C42C2×Q8×C2918yes—
185C42C2×Q8×C2914yes—
186C42#41×C29116yes—
187C23—24no—
188C23C22×Q8×C2912yes—
189C23C2×#41×C2914yes—
190C23C25×C2911yescharacteristic
191C2×C4—232no—
192C2×C4—24no—
193C2×C4—28no—
194C2×C4—28no—
195C2×C4—216no—
196C2×C4—216no—
197C2×C4—232no—
198C2×C4C29×#125116yescomplemented
199C2×C4C22×Q8×C2914yes—
200C2×C4C22×Q8×C2912yes—
201C2×C4C22×Q8×C2912yes—
202C2×C4C22×Q8×C2914yes—
203C2×C4C2×#41×C29116yes—
204C2×C4C2×#41×C2914yes—
205C2×C4C2×#41×C2914yes—
206C2×C4C2×#41×C2918yes—
207C22—24no—
208C22—28no—
209C22C2×C29×#12514yes—
210C22C23×Q8×C2911yescharacteristic
211C22C22×#41×C2914yes—
212C22C22×#41×C2912yes—
213C4—24no—
214C4—216no—
215C4—416no—
216C4C2×C29×#12514yes—
217C4C2×C29×#12514yes—
218C4C29×#53318yes—
219C2—24no—
220C2C22×C29×#12511yescharacteristic
221C2C2×C29×#53312yes—
222C2C29×#344414yes—
subgroupG/H
centerC22×C4×C29C24
commutator, Frattini, cosocleC23C25×C29
socleC23×C29C25
prime radicalC24×C29C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2864C2semidirect
2. C29×#2859C2semidirect
4. C4×C29×#125C2semidirect
75. #36640C29direct (N × H)
87. C2×C4×C29#125semidirect
96. #2864C2×C29semidirect
97. #2859C2×C29semidirect
99. C4×#125C2×C29semidirect
160. C29#36640direct (N × H)
198. C2×C4C29×#125semidirect

Maximal subgroups

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

subgroupindex
C29×#28642
C29×#28592
C29×#28512
C4×C29×#1252
C29×#22962
C29×#22852
C2×C43×C292
#3664029