Finite Group Databasebeta

← C29×#11449 #20306349

Subgroups — C29×#11449 #20306349

Order 7424.

434 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2317C211yesmaximal, characteristic
2C29×#1458C212yesmaximal
3C29×#1324C214yesmaximal, complemented
4C2×C29×#117C411yescharacteristic
5C2×C29×#117C2211yescharacteristic
6C22×C4⋊C4×C29C411yescharacteristic
7C29×#431—22no—
8C29×#389—22no—
9C29×#385—22no—
10C29×#384C412yes—
11C29×#382C2212yes—
12C29×#324C2214yes—
13C29×#323—22no—
14C23×C4×C29—21no—
15C23×C4×C29C2×C411yescharacteristic
16C29×#117—22no—
17C29×#117—42no—
18C29×#117C814yescomplemented
19C2×C4⋊C4×C29—21no—
20C2×C4⋊C4×C29—21no—
21C2×C4⋊C4×C29—24no—
22C2×C4⋊C4×C29—42no—
23C2×C4⋊C4×C29C2×C412yes—
24C2×C4⋊C4×C29C2×C411yescharacteristic
25C2×C4⋊C4×C29C2311yescharacteristic
26C2×C22⋊C4×C29—21no—
27C2×C22⋊C4×C29D412yes—
28C2×C42×C29C2×C412yes—
29C2×C42×C29D412yes—
30C29×C4⋊C8—42no—
31C29×C22⋊C8—24no—
32C4×C8×C29—42no—
33C29×#95—24no—
34C24×C29C22⋊C411yescharacteristic
35C22×C4×C29—22no—
36C22×C4×C29—22no—
37C22×C4×C29—22no—
38C22×C4×C29—22no—
39C22×C4×C29—42no—
40C22×C4×C29—82no—
41C22×C4×C29C22⋊C412yes—
42C22×C4×C29C22⋊C411yescharacteristic
43C22×C4×C29C2×C812yes—
44C22×C4×C29M1612yes—
45C22×C4×C29C22×C411yescharacteristic
46C22×C4×C29C2×D412yes—
47C2×C8×C29—44no—
48C4⋊C4×C29—24no—
49C4⋊C4×C29—41no—
50C4⋊C4×C29—41no—
51C4⋊C4×C29—42no—
52C4⋊C4×C29—42no—
53C4⋊C4×C29—84no—
54C22⋊C4×C29—24no—
55C22⋊C4×C29—42no—
56C42×C29—22no—
57C42×C29—22no—
58C42×C29—22no—
59C42×C29C2×C814yes—
60#11449C2911yesmaximal, characteristic, direct product factor, Sylow
61C23×C29—21no—
62C23×C29—21no—
63C23×C29—41no—
64C23×C29—41no—
65C23×C29C22⋊C812yes—
66C23×C29C2×C22⋊C411yescharacteristic
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29—24no—
70C2×C4×C29—24no—
71C2×C4×C29—24no—
72C2×C4×C29—22no—
73C2×C4×C29—22no—
74C2×C4×C29—42no—
75C2×C4×C29—42no—
76C2×C4×C29—42no—
77C2×C4×C29—42no—
78C2×C4×C29—44no—
79C2×C4×C29—42no—
80C2×C4×C29—84no—
81C2×C4×C29C22⋊C812yes—
82C2×C4×C29#9912yes—
83C2×C4×C29#10112yes—
84C2×C4×C29C22×C811yescharacteristic
85C2×C4×C29C2×M1611yescharacteristic
86C8×C29—84no—
87#2317C2×C2911yescharacteristic
88#1458C2×C2912yes—
89#1324C2×C2914yescomplemented
90C22×C29—21no—
91C22×C29—21no—
92C22×C29—22no—
93C22×C29—42no—
94C22×C29—42no—
95C22×C29—41no—
96C22×C29—41no—
97C22×C29C2×C22⋊C811yescharacteristic
98C22×C29C2×#9911yescharacteristic
99C22×C29C2×#10111yescharacteristic
100C4×C29—21no—
101C4×C29—21no—
102C4×C29—44no—
103C4×C29—42no—
104C4×C29—42no—
105C4×C29—82no—
106C4×C29#32414yes—
107C2×#117C4×C2911yescharacteristic
108C2×#117C22×C2911yescharacteristic
109C22×C4⋊C4C4×C2911yescharacteristic
110#431—22no—
111#389—22no—
112#385—22no—
113#384C4×C2912yes—
114#382C22×C2912yes—
115#324C22×C2914yes—
116#323—22no—
117C2×C29—21no—
118C2×C29—21no—
119C2×C29—42no—
120C2×C29C2×#32411yescharacteristic
121C2×C29#212911yescharacteristic
122C2×C29#213411yescharacteristic
123C23×C4—21no—
124C23×C4C2×C4×C2911yescharacteristic
125#117—22no—
126#117—42no—
127#117C8×C2914yescomplemented
128C2×C4⋊C4—21no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4C2×C4×C2912yes—
133C2×C4⋊C4C2×C4×C2911yescharacteristic
134C2×C4⋊C4C23×C2911yescharacteristic
135C2×C22⋊C4—21no—
136C2×C22⋊C4D4×C2912yes—
137C2×C42C2×C4×C2912yes—
138C2×C42D4×C2912yes—
139C4⋊C8—42no—
140C22⋊C8—24no—
141C4×C8—42no—
142#95—24no—
143C29#1144911yescharacteristic, direct product factor, Sylow
144C24C22⋊C4×C2911yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—82no—
151C22×C4C22⋊C4×C2912yes—
152C22×C4C22⋊C4×C2911yescharacteristic
153C22×C4C2×C8×C2912yes—
154C22×C4M16×C2912yes—
155C22×C4C22×C4×C2911yescharacteristic
156C22×C4C2×D4×C2912yes—
157C2×C8—44no—
158C4⋊C4—24no—
159C4⋊C4—41no—
160C4⋊C4—41no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—84no—
164C22⋊C4—24no—
165C22⋊C4—42no—
166C42—22no—
167C42—22no—
168C42—22no—
169C42C2×C8×C2914yes—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23C29×C22⋊C812yes—
175C23C2×C22⋊C4×C2911yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—44no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4C29×C22⋊C812yes—
191C2×C4C29×#9912yes—
192C2×C4C29×#10112yes—
193C2×C4C22×C8×C2911yescharacteristic
194C2×C4C2×M16×C2911yescharacteristic
195C8—84no—
196C22—21no—
197C22—21no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22C2×C29×C22⋊C811yescharacteristic
204C22C2×C29×#9911yescharacteristic
205C22C2×C29×#10111yescharacteristic
206C4—21no—
207C4—21no—
208C4—44no—
209C4—42no—
210C4—42no—
211C4—82no—
212C4C29×#32414yes—
213C2—21no—
214C2—21no—
215C2—42no—
216C2C2×C29×#32411yescharacteristic
217C2C29×#212911yescharacteristic
218C2C29×#213411yescharacteristic
subgroupG/H
center, socleC22×C29C2×#99
commutatorC2×C4C22×C8×C29
Frattini, cosocleC2×C4⋊C4C23×C29
prime radicalC24×C29C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1324C2semidirect
18. C29×#117C8semidirect
60. #11449C29direct (N × H)
89. #1324C2×C29semidirect
127. #117C8×C29semidirect
143. C29#11449direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23172
C29×#14582
C29×#13242
#1144929