Finite Group Databasebeta

← C29×#8735 #20303635

Subgroups — C29×#8735 #20303635

Order 7424.

514 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 166 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×#2274C211yesmaximal, characteristic
2C2×C29×#324C212yesmaximal
3C29×#1282C214yesmaximal
4C2×C29×#117C411yescharacteristic
5C2×C29×#117C411yescharacteristic
6C22×C4⋊C4×C29C2211yescharacteristic
7C2×C29×C22⋊C8C2214yes—
8C4×C4⋊C4×C29—22no—
9C4×C4⋊C4×C29—22no—
10C4×C22⋊C4×C29C412yes—
11C4×C22⋊C4×C29C2212yes—
12C29×#324—22no—
13C29×#324—22no—
14C23×C4×C29C2×C411yescharacteristic
15C23×C4×C29C2×C411yescharacteristic
16C23×C4×C29C2311yescharacteristic
17C22×C8×C29—24no—
18C29×#117—22no—
19C29×#117—24no—
20C29×#117C814yescomplemented
21C2×C4⋊C4×C29—21no—
22C2×C4⋊C4×C29—21no—
23C2×C4⋊C4×C29—24no—
24C2×C4⋊C4×C29D412yes—
25C2×C4⋊C4×C29D412yes—
26C2×C22⋊C4×C29C2×C412yes—
27C2×C22⋊C4×C29C2×C412yes—
28C2×C42×C29—21no—
29C2×C42×C29—21no—
30C2×C42×C29—22no—
31C2×C42×C29—22no—
32C29×C22⋊C8—24no—
33C29×C22⋊C8—24no—
34C29×#95—22no—
35C29×#95—22no—
36C24×C29C22×C411yescharacteristic
37C22×C4×C29—22no—
38C22×C4×C29—22no—
39C22×C4×C29—22no—
40C22×C4×C29—22no—
41C22×C4×C29—22no—
42C22×C4×C29—81no—
43C22×C4×C29—81no—
44C22×C4×C29C22⋊C411yescharacteristic
45C22×C4×C29C22⋊C411yescharacteristic
46C22×C4×C29C22⋊C412yes—
47C22×C4×C29C2×C812yes—
48C22×C4×C29M1612yes—
49C22×C4×C29C2×D412yes—
50C22×C4×C29#4114yes—
51C2×C8×C29—44no—
52C2×C8×C29—84no—
53C4⋊C4×C29—24no—
54C4⋊C4×C29—24no—
55C4⋊C4×C29—24no—
56C4⋊C4×C29—24no—
57C22⋊C4×C29—22no—
58C22⋊C4×C29—22no—
59C22⋊C4×C29C2×C814yes—
60C22⋊C4×C29M1614yes—
61C42×C29—24no—
62C42×C29—24no—
63C42×C29—82no—
64C42×C29—82no—
65#8735C2911yesmaximal, characteristic, direct product factor, Sylow
66C23×C29—41no—
67C23×C29—41no—
68C23×C29C2×C22⋊C411yescharacteristic
69C23×C29#11712yes—
70C23×C29C22×C811yescharacteristic
71C23×C29C2×M1611yescharacteristic
72C23×C29C2×M1612yes—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29—21no—
76C2×C4×C29—21no—
77C2×C4×C29—24no—
78C2×C4×C29—24no—
79C2×C4×C29—22no—
80C2×C4×C29—24no—
81C2×C4×C29—24no—
82C2×C4×C29—42no—
83C2×C4×C29—44no—
84C2×C4×C29—42no—
85C2×C4×C29—42no—
86C2×C4×C29—42no—
87C2×C4×C29—42no—
88C2×C4×C29—42no—
89C2×C4×C29—82no—
90C2×C4×C29C22⋊C812yes—
91C2×C4×C29C22⋊C812yes—
92C2×C4×C29#12314yes—
93C8×C29—84no—
94#2274C2×C2911yescharacteristic
95C2×#324C2×C2912yes—
96#1282C2×C2914yes—
97C22×C29—21no—
98C22×C29—22no—
99C22×C29—21no—
100C22×C29—22no—
101C22×C29—41no—
102C22×C29—41no—
103C22×C29—42no—
104C22×C29#38111yescharacteristic
105C22×C29C2×C22⋊C811yescharacteristic
106C22×C29#40711yescharacteristic
107C22×C29#43112yes—
108C22×C29#43212yes—
109C4×C29—22no—
110C4×C29—22no—
111C4×C29—24no—
112C4×C29—44no—
113C4×C29—44no—
114C4×C29—42no—
115C2×#117C4×C2911yescharacteristic
116C2×#117C4×C2911yescharacteristic
117C22×C4⋊C4C22×C2911yescharacteristic
118C2×C22⋊C8C22×C2914yes—
119C4×C4⋊C4—22no—
120C4×C4⋊C4—22no—
121C4×C22⋊C4C4×C2912yes—
122C4×C22⋊C4C22×C2912yes—
123#324—22no—
124#324—22no—
125C2×C29—21no—
126C2×C29—21no—
127C2×C29—22no—
128C2×C29—22no—
129C2×C29#181711yescharacteristic
130C2×C29#182811yescharacteristic
131C2×C29#183011yescharacteristic
132C23×C4C2×C4×C2911yescharacteristic
133C23×C4C2×C4×C2911yescharacteristic
134C23×C4C23×C2911yescharacteristic
135C22×C8—24no—
136#117—22no—
137#117—24no—
138#117C8×C2914yescomplemented
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—24no—
142C2×C4⋊C4D4×C2912yes—
143C2×C4⋊C4D4×C2912yes—
144C2×C22⋊C4C2×C4×C2912yes—
145C2×C22⋊C4C2×C4×C2912yes—
146C2×C42—21no—
147C2×C42—21no—
148C2×C42—22no—
149C2×C42—22no—
150C22⋊C8—24no—
151C22⋊C8—24no—
152#95—22no—
153#95—22no—
154C29#873511yescharacteristic, direct product factor, Sylow
155C24C22×C4×C2911yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—81no—
162C22×C4—81no—
163C22×C4C22⋊C4×C2911yescharacteristic
164C22×C4C22⋊C4×C2911yescharacteristic
165C22×C4C22⋊C4×C2912yes—
166C22×C4C2×C8×C2912yes—
167C22×C4M16×C2912yes—
168C22×C4C2×D4×C2912yes—
169C22×C4#41×C2914yes—
170C2×C8—44no—
171C2×C8—84no—
172C4⋊C4—24no—
173C4⋊C4—24no—
174C4⋊C4—24no—
175C4⋊C4—24no—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C22⋊C4C2×C8×C2914yes—
179C22⋊C4M16×C2914yes—
180C42—24no—
181C42—24no—
182C42—82no—
183C42—82no—
184C23—41no—
185C23—41no—
186C23C2×C22⋊C4×C2911yescharacteristic
187C23C29×#11712yes—
188C23C22×C8×C2911yescharacteristic
189C23C2×M16×C2912yes—
190C23C2×M16×C2911yescharacteristic
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—82no—
208C2×C4C29×C22⋊C812yes—
209C2×C4C29×C22⋊C812yes—
210C2×C4C29×#12314yes—
211C8—84no—
212C22—21no—
213C22—22no—
214C22—21no—
215C22—22no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22C29×#38111yescharacteristic
220C22C2×C29×C22⋊C811yescharacteristic
221C22C29×#40711yescharacteristic
222C22C29×#43112yes—
223C22C29×#43212yes—
224C4—22no—
225C4—22no—
226C4—24no—
227C4—44no—
228C4—44no—
229C4—42no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2C29×#181711yescharacteristic
235C2C29×#182811yescharacteristic
236C2C29×#183011yescharacteristic
subgroupG/H
center, socleC22×C29#381
commutatorC23C22×C8×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC24×C29C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
20. C29×#117C8semidirect
65. #8735C29direct (N × H)
138. #117C8×C29semidirect
154. C29#8735direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#22742
C2×C29×#3242
C29×#12822
#873529