Finite Group Databasebeta

← C29×#1794 #16815508

Subgroups — C29×#1794 #16815508

Order 3712.

548 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 132 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×#585C211yesmaximal, characteristic
2C29×#421C212yesmaximal, complemented
3C29×#416C212yesmaximal, complemented
4C29×#410C211yesmaximal, characteristic, complemented
5C29×#408C211yesmaximal, characteristic, complemented
6C29×2−1+4—22no—
7C29×2−1+4C412yescomplemented
8C29×H(5,𝔽2)—22no—
9C29×H(5,𝔽2)—22no—
10C29×H(5,𝔽2)C412yescomplemented
11C2×#41×C29—24no—
12C2×#41×C29—22no—
13C2×#41×C29C2212yes—
14C2×#41×C29C2211yescharacteristic
15C2×M16×C29C2211yescharacteristic, complemented
16C22×C8×C29C2211yescharacteristic, complemented
17C29×#117C2212yescomplemented
18C29×#104—24no—
19C29×#103—22no—
20C29×#102—22no—
21C29×#99—22no—
22C29×C22⋊C8—22no—
23#41×C29—24no—
24#41×C29—28no—
25#41×C29—24no—
26#41×C29—24no—
27#41×C29—24no—
28#41×C29—24no—
29#41×C29—22no—
30#41×C29—22no—
31#41×C29—22no—
32#41×C29—22no—
33#41×C29C2×C414yes—
34#41×C29D414yes—
35C2×Q8×C29—22no—
36C2×Q8×C29—24no—
37C2×Q8×C29C2×C411yescharacteristic
38C2×Q8×C29D412yes—
39C2×D4×C29—28no—
40C2×D4×C29—22no—
41C2×D4×C29—24no—
42C2×D4×C29—22no—
43C2×D4×C29—24no—
44C2×D4×C29C2×C411yescharacteristic
45C2×D4×C29D412yes—
46C2×D4×C29D412yes—
47C22×C4×C29—24no—
48C22×C4×C29—22no—
49C22×C4×C29D412yes—
50C22×C4×C29C2311yescharacteristic
51M16×C29—22no—
52C2×C8×C29—21no—
53C2×C8×C29—22no—
54C2×C8×C29—21no—
55C4⋊C4×C29—22no—
56C22⋊C4×C29—22no—
57C42×C29—22no—
58C23×C29—24no—
59C23×C29—22no—
60C23×C29C22⋊C412yes—
61C23×C29C2×D411yescharacteristic
62Q8×C29—24no—
63Q8×C29—22no—
64Q8×C29—22no—
65Q8×C29C22⋊C414yes—
66D4×C29—28no—
67D4×C29—24no—
68D4×C29—24no—
69D4×C29—24no—
70D4×C29—24no—
71D4×C29—22no—
72D4×C29—22no—
73D4×C29C22⋊C414yes—
74C2×C4×C29—24no—
75C2×C4×C29—28no—
76C2×C4×C29—22no—
77C2×C4×C29—24no—
78C2×C4×C29—22no—
79C2×C4×C29—24no—
80C2×C4×C29—22no—
81C2×C4×C29—42no—
82C2×C4×C29C22⋊C412yes—
83C2×C4×C29C22×C411yescharacteristic
84C2×C4×C29C2×D412yes—
85C2×C4×C29C2×D412yes—
86C2×C4×C29C2×D411yescharacteristic
87C8×C29—41no—
88C8×C29—41no—
89#1794C2911yesmaximal, characteristic, direct product factor, Sylow
90C22×C29—22no—
91C22×C29—24no—
92C22×C29—41no—
93C22×C29—42no—
94C22×C29—82no—
95C22×C29—84no—
96C22×C29C2×C22⋊C411yescharacteristic
97C22×C29#12012yes—
98C4×C29—24no—
99C4×C29—22no—
100C4×C29—82no—
101C4×C29C2×C22⋊C412yes—
102C4×C29#12011yescharacteristic
103C4×C29#12011yescharacteristic
104#585C2×C2911yescharacteristic
105#421C2×C2912yescomplemented
106#416C2×C2912yescomplemented
107#410C2×C2911yescharacteristic, complemented
108#408C2×C2911yescharacteristic, complemented
109C2×C29—22no—
110C2×C29—21no—
111C2×C29—42no—
112C2×C29—44no—
113C2×C29#37911yescharacteristic
1142−1+4—22no—
1152−1+4C4×C2912yescomplemented
116H(5,𝔽2)—22no—
117H(5,𝔽2)—22no—
118H(5,𝔽2)C4×C2912yescomplemented
119C2×#41—24no—
120C2×#41—22no—
121C2×#41C22×C2912yes—
122C2×#41C22×C2911yescharacteristic
123C2×M16C22×C2911yescharacteristic, complemented
124C22×C8C22×C2911yescharacteristic, complemented
125#117C22×C2912yescomplemented
126#104—24no—
127#103—22no—
128#102—22no—
129#99—22no—
130C22⋊C8—22no—
131C29#179411yescharacteristic, direct product factor, Sylow
132#41—24no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—24no—
137#41—24no—
138#41—22no—
139#41—22no—
140#41—22no—
141#41—22no—
142#41C2×C4×C2914yes—
143#41D4×C2914yes—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8C2×C4×C2911yescharacteristic
147C2×Q8D4×C2912yes—
148C2×D4—28no—
149C2×D4—22no—
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—24no—
153C2×D4C2×C4×C2911yescharacteristic
154C2×D4D4×C2912yes—
155C2×D4D4×C2912yes—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4D4×C2912yes—
159C22×C4C23×C2911yescharacteristic
160M16—22no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—22no—
164C4⋊C4—22no—
165C22⋊C4—22no—
166C42—22no—
167C23—24no—
168C23—22no—
169C23C22⋊C4×C2912yes—
170C23C2×D4×C2911yescharacteristic
171Q8—24no—
172Q8—22no—
173Q8—22no—
174Q8C22⋊C4×C2914yes—
175D4—28no—
176D4—24no—
177D4—24no—
178D4—24no—
179D4—24no—
180D4—22no—
181D4—22no—
182D4C22⋊C4×C2914yes—
183C2×C4—24no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4C22⋊C4×C2912yes—
192C2×C4C22×C4×C2911yescharacteristic
193C2×C4C2×D4×C2912yes—
194C2×C4C2×D4×C2912yes—
195C2×C4C2×D4×C2911yescharacteristic
196C8—41no—
197C8—41no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—84no—
204C22C2×C22⋊C4×C2911yescharacteristic
205C22C29×#12012yes—
206C4—24no—
207C4—22no—
208C4—82no—
209C4C2×C22⋊C4×C2912yes—
210C4C29×#12011yescharacteristic
211C4C29×#12011yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—44no—
216C2C29×#37911yescharacteristic
subgroupG/H
centerC4×C29#120
commutatorC2×C4C22×C4×C29
Frattini, cosocleC22×C4C23×C29
socleC2×C29#379
prime radicalC29×#585C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C29 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#421C2semidirect
3. C29×#416C2semidirect
4. C29×#410C2semidirect
5. C29×#408C2semidirect
7. C29×2−1+4C4semidirect
10. C29×H(5,𝔽2)C4semidirect
15. C2×M16×C29C22semidirect
16. C22×C8×C29C22semidirect
17. C29×#117C22semidirect
89. #1794C29direct (N × H)
105. #421C2×C29semidirect
106. #416C2×C29semidirect
107. #410C2×C29semidirect
108. #408C2×C29semidirect
115. 2−1+4C4×C29semidirect
118. H(5,𝔽2)C4×C29semidirect
123. C2×M16C22×C29semidirect
124. C22×C8C22×C29semidirect
125. #117C22×C29semidirect
131. C29#1794direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5852
C29×#4212
C29×#4162
C29×#4102
C29×#4082
#179429